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Hidden Link Prediction
in Stochastic Social
Networks
Babita Pandey
Lovely Professional University, India
Aditya Khamparia
A volume in the Advances in
Social Networking and Online
Communities (ASNOC) Book Series

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Title: Hidden link prediction in stochastic social networks / Babita Pandey
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Identifiers: LCCN 2018057677| ISBN 9781522590965 (hardcover) | ISBN
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Cognitive Social Mining Applications in Data Analytics and Forensics
Anandakumar Haldorai (Sri Eshwar College of Engineering, India) and Arulmurugan Ramu
(Presidency Universiy, India)
InformationScienceReference•©2019•326pp•H/C(ISBN:9781522575221)•US$195.00
Modern Perspectives on Virtual Communications and SocialNetworking
Jyotsana Thakur (Amity University, India)
Exploring the Role of Social Media in Transnational Advocacy
Floribert Patrick C. Endong (University of Calabar, Nigeria)
Online Communities as Agents of Change and Social Movements
Steven Gordon (Babson College, USA)
Social Media Performance Evaluation and Success Measurements
Michael A. Brown Sr. (Florida International University, USA)
Political Scandal, Corruption, and Legitimacy in the Age of Social Media
Kamil Demirhan (Bülent Ecevit University, Turkey) and Derya Çakır-Demirhan (Bülent
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Editorial Advisory Board
Mayank Agrawal, Gurukul Kangri University, India
Sami Al Radaei, Hajjah University, Yemen
Sandeep Kumar Garg, IIT Roorkee, India
Ashutosh Mishra, Thapar University, India
R. B. Mishra, IIT BHU, India
Vimal Mishra, IERT Prayagraj, India
Aman Singh, Lovely Professional University, India
Shailendra Tiwari, Trinity University Dublin, Ireland
Sudhakar Tripathi, IIT Patna, India

Table of Contents
Preface.
................................................................................................................. xv
Acknowledgment................................................................................................xxi
Chapter 1
Similarity-Based Indices or Metrics for Link Prediction.
.......................................1
Praveen Kumar Bhanodia, Lovely Professional University, India
Kamal Kumar Sethi, Acropolis Institute of Technology and Research,
India
Aditya Khamparia, Lovely Professional University, India
Babita Pandey, Babasaheb Bhimrao Ambedkar University, India
Shaligram Prajapat, IIPS DAV, India
Chapter 2
Application and Impact of Social Network in Modern Society............................30
Mamata Rath, Birla Global University, India
Chapter 3
Online Social Network Analysis...........................................................................50
Chapter 4
Position Independent Mobile User Authentication Using Keystroke .
Dynamics..............................................................................................................64
Baljit Singh Saini, Lovely Professional University, India & Sri Guru
Granth Sahib World University, India
Navdeep Kaur, Sri Guru Granth Sahib World University, India
Kamaljit Singh Bhatia, IKGPTU, India

Chapter 5
Drug Prediction in Healthcare Using Big Data and Machine Learning...............79
Mamoon Rashid, Lovely Professional University, India & Punjabi
University, India
Vishal Goyal, Punjabi University, India
Shabir Ahmad Parah, University of Kashmir, India
Harjeet Singh, Mata Gujri College, India
Chapter 6
Analysis of Access Delay in Ad Hoc Wireless Networks for Multimedia
Applications..........................................................................................................93
Arundhati Arjaria, Rajiv Gandhi Proudyogiki Vishwavidyalaya, India
Chapter 7
Deep Learning: An Overview and Innovative Approach in Machine .
Learning..............................................................................................................108
Amit Sinha, ABES Engineering College, India
Suneet Kumar Gupta, Bennett University, India
Anurag Tiwari, Indian Institute of Technology (BHU), India
Amrita Chaturvedi, Indian Institute of Technology (BHU), India
Chapter 8
Delay Tolerant Networks Architecture, Protocols, and Its Application in
Vehicular Ad-Hoc Networks...............................................................................135
Vijander Singh, Amity University Rajasthan, India
Linesh Raja, Amity University Rajasthan, India
Deepak Panwar, Amity University Rajasthan, India
Pankaj Agarwal, Amity University Rajasthan, India
Chapter 9
Digital Image Classification Techniques: A Comprehensive Review................162
Utkarsh Shrivastav, Lovely Professional University, India
Sanjay Kumar Singh, Lovely Professional University, India
Chapter 10
Intelligent Medical Diagnostic System for Diabetes.
..........................................188
Jimmy Singla, Lovely Professional University, India

Compilation of References............................................................................... 210
Related References............................................................................................ 240
About the Contributors.................................................................................... 273
Index................................................................................................................... 279

Detailed Table of Contents
Preface.
................................................................................................................. xv
Acknowledgment................................................................................................xxi
Chapter 1
Similarity-Based Indices or Metrics for Link Prediction.
.......................................1
Kamal Kumar Sethi, Acropolis Institute of Technology and Research,
India
Link prediction in social network has gained momentum with the inception of
machine learning. The social networks are evolving into smart dynamic networks
possessing various relevant information about the user. The relationship between
users can be approximated by evaluation of similarity between the users. Online
social network (OSN) refers to the formulation of association (relationship/links)
between users known as nodes. Evolution of OSNs such as Facebook, Twitter,
Hi-Fi, LinkedIn has provided a momentum to the growth of such social networks,
whereby millions of users are joining it. The online social network evolution has
motivated scientists and researchers to analyze the data and information of OSN
in order to recommend the future friends. Link prediction is a problem instance of
such recommendation systems. Link prediction is basically a phenomenon through
which potential links between nodes are identified on a network over the period of
time. In this chapter, the authors describe the similarity metrics that further would
be instrumental in recognition of future links between nodes.

Chapter 2
Application and Impact of Social Network in Modern Society............................30
Mamata Rath, Birla Global University, India
Social network and its corresponding website permits a client to make a profile, set
up an authorized account to create a digital representation of themselves, to select
other members of the site as contacts, make connections with them, communicate
and engage with these users in different social activities, etc. So, social network
includes details of persons, group details, their friends list, contact list, business,
affiliations, personal data, personal preferences, and historical information. In this
age of smart communication and technology, most of the time people are connected
with mobile smart telephones in their work culture, home, office, or any other related
places. As they are constantly associated with social systems for long time, they get
new posts, messages, and current refreshed news readily available in a flash. This
is the constructive part of social networking that individuals consistently remain
refreshed with most recent news and innovation. This chapter presents an overview
of social network design, various issues, and emerging trends that are evolved
simultaneously with modern age. It also presents a detail study on application and
impact of social network in modern society as well as exhibits an exhaustive review
of security measures in social sites.
Chapter 3
Online Social Network Analysis...........................................................................50
Expansion of online social networks is rapid and furious. Millions of users are
appending to it and enriching the nature and behavior, and the information generated
has various dimensional properties providing new opportunities and perspective for
computation of network properties. The structure of social networks is comprised
of nodes and edges whereas users are entities represented by node and relationships
designated by edges. Processing of online social networks structural features yields
fairknowledgewhichcanbeusedinmanyofrecommendationandpredictionsystems.
This is referred to as social network analysis, and the features exploited usually are
local and global both plays significant role in processing and computation. Local
features include properties of nodes like degree of the node (in-degree, out-degree)
whileglobalfeatureprocessthepathbetweennodesintheentirenetwork.Thechapter
is an effort in the direction of online social network analysis that explores the basic
methods that can be process and analyze the network with a suitable approach to
yield knowledge.

Chapter 4
Position Independent Mobile User Authentication Using Keystroke .
Dynamics..............................................................................................................64
Baljit Singh Saini, Lovely Professional University, India & Sri Guru
Granth Sahib World University, India
Navdeep Kaur, Sri Guru Granth Sahib World University, India
Kamaljit Singh Bhatia, IKGPTU, India
In this chapter, a novel technique to authenticate a mobile phone user irrespective
of his/her typing position is presented. The user is never always in sitting position
while using mobile phone. Thus, it becomes very important to check the accuracy of
keystroke dynamics technique while taking input in all positions but authenticating
theuserirrespectiveofthesepositions.Threeuserpositionswereconsideredforinput
– sitting, walking, and relaxed. The input was taken in uncontrolled environment to
getrealisticresults.Holdtime,latency,andmotionfeaturesusingaccelerometerdata
were extracted, and the analysis was done using random forest and KNN classifiers.
The accelerometer data provides additional features like mean of all X, Y, and Z axis
values. The inclusion of these features improved the results drastically and played a
very significant role in determining the user typing behavior. An EER of 4.3% was
achieved with a best FAR of 0.9% and an FRR of 15.2%.
Chapter 5
Drug Prediction in Healthcare Using Big Data and Machine Learning...............79
Mamoon Rashid, Lovely Professional University, India & Punjabi
University, India
Vishal Goyal, Punjabi University, India
Shabir Ahmad Parah, University of Kashmir, India
Harjeet Singh, Mata Gujri College, India
Thehealthcaresystemisliterallylosingpatientsduetoimproperdiagnosis,accidents,
andinfectionsinhospitalsalone.Toaddressthesechallenges,theauthorsareproposing
the drug prediction model that will act as informative guide for patients and help
them for taking right medicines for the cure of particular disease. In this chapter,
the authors are proposing use of Hadoop distributed file system for the storage of
medical datasets related to medicinal drugs. MLLib Library of Apache Spark is to
be used for initial data analysis for drug suggestions related to symptoms gathered
from particular user. The model will analyze the previous history of patients for any
side effects of the drug to be recommended. This proposal will consider weather and
maps API from Google as well so that the patients can easily locate the nearby stores
where the medicines will be available. It is believed that this proposal of research
will surely eradicate the issues by prescribing the optimal drug and its availability
by giving the location of the retailer of that drug near the customer.

Chapter 6
Analysis of Access Delay in Ad Hoc Wireless Networks for Multimedia
Applications..........................................................................................................93
Arundhati Arjaria, Rajiv Gandhi Proudyogiki Vishwavidyalaya, India
Mobile ad hoc networks are infrastructure-less wireless networks; all nodes can
quickly share information without using any fixed infrastructure like base station
or access point. Wireless ad hoc networks are characterized by frequent topology
changes, unreliable wireless channel, network congestion, and resource contention.
Multimediaapplicationsusuallyarebandwidthhungrywithstringentdelay,jitter,and
lossrequirements.Designingadhocnetworkswhichsupportmultimediaapplications,
hence, is considered a hard task. The hidden and exposed terminal problems are
the main which consequently reduces the network capacity. Hidden and exposed
nodes reduce the performance of the wireless ad hoc networks. Access delay is the
major parameter that is to be taken under consideration. Due to hidden and exposed
terminal problems, the network suffers from a serious unfairness problem.
Chapter 7
Deep Learning: An Overview and Innovative Approach in Machine .
Learning..............................................................................................................108
Amit Sinha, ABES Engineering College, India
Suneet Kumar Gupta, Bennett University, India
Anurag Tiwari, Indian Institute of Technology (BHU), India
Amrita Chaturvedi, Indian Institute of Technology (BHU), India
Deep learning approaches have been found to be suitable for the agricultural field
with successful applications to vegetable infection through plant disease. In this
chapter, the authors discuss some widely used deep learning architecture and their
practical applications. Nowadays, in many typical applications of machine vision,
there is a tendency to replace classical techniques with deep learning algorithms.
The benefits are valuable; on one hand, it avoids the need of specialized handcrafted
features extractors, and on the other hand, results are not damaged. Moreover, they
typically get improved.
Chapter 8
Delay Tolerant Networks Architecture, Protocols, and Its Application in
Vehicular Ad-Hoc Networks...............................................................................135
Vijander Singh, Amity University Rajasthan, India
Linesh Raja, Amity University Rajasthan, India
Deepak Panwar, Amity University Rajasthan, India
Pankaj Agarwal, Amity University Rajasthan, India
Due to the high mobility of vehicular nodes in VANETs, there are high chances of
partitions in the network. In such a situation, the protocols developed for VANETs

cannot work well and an alternative network known as DTN (delay tolerant network)
is capable enough to deal with VANET characteristics. The network which does
not need any immediate data delivery and can wait for time and delivery of data
is known as DTN. The concept of hold and forward the message is exploited by
DTN. In this chapter, the authors are providing characteristics, architecture, and
applications of delay tolerant vehicular ad-hoc networks.
Chapter 9
Digital Image Classification Techniques: A Comprehensive Review................162
Utkarsh Shrivastav, Lovely Professional University, India
Sanjay Kumar Singh, Lovely Professional University, India
Image classification is a technique to categorize an image in to given classes on the
basis of hidden characteristics or features extracted using image processing. With
rapidly growing technology, the size of images is growing. Different categories of
images may contain different types of hidden information such as x-ray, CT scan,
MRI, pathologies images, remote sensing images, satellite images, and natural
scene image captured via digital cameras. In this chapter, the authors have surveyed
various articles and books and summarized image classification techniques. There
are supervised techniques like KNN and SVM, which classify an image into given
classes and unsupervised techniques like K-means and ISODATA for classifying
image into a group of clusters. For big images, deep learning networks can be
employed that are fast and efficient and also compute hidden features automatically.
Chapter 10
Intelligent Medical Diagnostic System for Diabetes.
..........................................188
Jimmy Singla, Lovely Professional University, India
In this chapter, the neuro-fuzzy technique has been used for the diagnosis of different
types of diabetes. It has been reported in the literature that triangular membership
functions have been deployed for Mamdani and Sugeno fuzzy expert systems that
havebeenusedfordiagnosisofdifferenttypesofdiabetes.TheGaussianmembership
functions are expected to give better results. In this context, Gaussian membership
functionshavebeenattemptedintheneuro-fuzzysystemforthediagnosisofdifferent
types of diabetes in the research work, and improved results have been obtained in
termsofdifferentparameterslikesensitivity,specificity,accuracy,precision.Further,
for the comparative study, the dataset used for neuro-fuzzy expert system developed
in this research work has been considered on Mamdani fuzzy expert system as well
as Sugeno fuzzy expert system, and it has been confirmed that the result parameters
show better values in the proposed model.

Preface
The tremendous growth of social networks has attracted lots of attention
from academia as well as industry due to its use in various applications such
as: friend recommendation, product recommendation, community detection,
collaborations etc. In fact, the stochastic growth of the social network leads to
variouschallengesinidentifyinghiddenlinksuchas:representationofgraph,
distinction between spurious and missing link, selection of link prediction
techniquesandnetworkfeatures,andtypeofnetwork.Thesocialnetworksare
evolvingintosmartdynamicnetworkspossessingvariousrelevantinformation
about the user. Link prediction in social network has gained momentum with
theinceptionofmachineLearning.Thepurposeofthisbookistodisseminate
cutting-edge research results, highlight research challenges and open issues,
and promotes further research interest and activities in identifying missing
linkinstochasticsocialnetworking.Inadditiontothisthisbookalsodiscusses
about the application of various machine learning techniques and problems
of various types of network such as: delay network.
BOOK OBJECTIVES
ThisbookconcentratesontheforemosttechniquesofHiddenLinkpredictions
in Stochastic Social Networks. It deals, principally, with methods and
approaches that involve similarity index techniques, matrix factorization,
reinforcement models, graph representations and community detections etc.
As well as, it will include the miscellaneous methods of different modalities
in deep learning, agent driven AI techniques and Automata driven systems.
Thisbookwillendeavourtoendowwithsignificantframeworksandthelatest
empirical research findings in the area. It will be written for professionals
whodesiretoimprovetheirunderstandinganddevelopingautomatedmachine
learning systems for supervised, unsupervised and recommendation driven
xv

Preface
learning systems. As, the progressions of this field will help to intensify
interdisciplinary discovery in e-commerce product recommendations,
community detection, Facebook predictions and friend recommendations,
credit score assignments. Anticipating linkages among information items
is a crucial information mining undertaking in different application spaces,
including recommender frameworks, data recovery, programmed Web
hyperlink era, record linkage, and correspondence observation.
TARGET AUDIENCE
The target audience of this book will be composed of professionals and
researchersworkinginthefieldofArtificialIntelligenceandSocialNetworks
invariousdisciplines,e.g.OnlineBookStorenetwork,dynamicsocialnetwork,
complex networks, relational graph driven networks, Bayesian networks,
predictive networks, researchers, academicians, advanced-level students,
technologydevelopersandDataScientists.Furthermore,thebookwillprovide
insights and support executives concerned with recent Artificial Intelligence
Systemsthathavemagnetizedmuchattentionasadvancedmachinecomputing
and devoted to use similarity techniques, predictive techniques, Automata,
proximity measure, time series, matrix factorization, reinforcement learning,
classification and clustering techniques.
ORGANIZATION
Chapter1describesthesimilaritymetricswhichfurtherwouldbeinstrumental
inrecognitionoffuturelinksbetweennodes.Insocialnetworktherelationship
between users can be predicted by measuring the similarity index between
the users. Online social network is represented as a graph and the node
in a graphs are user in social network. The link prediction formulates the
association (relationship/links) between users. Social Networks such as:
face-book, Twitter, Hi-Fi, Linkdln has provided a momentum to the growth
of networks by adding millions of users. This growth in social network has
motivated scientists and researchers to analyze the data and information of
social network in order to recommend the future friends. Link prediction is
probleminstanceofsuchrecommendationsystems.Linkpredictionisbasically
a phenomenon through which potential links between nodes is identified on
a network over the period of time.
xvi

Preface
Chapter 2 discussed about the various application and Impact of Social
Network in Modern Society. This chapter presents an overview of social
network design, various issues and emerging trends that are evolved
simultaneously with modern age. This chapter also exhibits an exhaustive
review of various impact of social network on modern society. In current
technological era, gadgets are easily available at cheap cost. Almost every
people have the mobile phone they use theses mobile phones in their work
culture and constantly associated with social systems for long time. Due to
which every second they get new posts, messages and current refreshed news
readily available in a flash. This is the constructive part of social networking
that individuals dependably remain refreshed with most recent news and
innovation.
In Chapter 3 we have analyse the online social network to explore the
basic methods that can be process the network with a suitable approach to
yield knowledge. The growth of online social networks is rapid and furious,
daily millions of users are joining to it. The information generated from social
networkhasvariousdimensionalpropertieswhichprovidenewopportunities
and perspective for computation of network properties. The social networks
consist of nodes and edges whereas users are entities represented by node
and relationships designated by edges. Processing of online social networks
structural features yields fair knowledge which can be used in many of
recommendation and prediction systems. The features exploited usually are
local and global both plays significant role in processing and computation.
Localfeaturesincludespropertiesofnodeslikedegreeofthenode(in-degree,
out-degree) while global feature process the path between nodes in the entire
network.
Chapter 4 presents a novel technique to authenticate a mobile phone user
irrespective of his/her typing position. The user is never always in sitting
position while using mobile phone. Thus, it becomes very important to
check the accuracy of keystroke dynamics technique while taking input in
all positions but authenticating the user irrespective of these positions. Three
user positions were considered for input – sitting, walking and relaxed. The
input was taken in uncontrolled environment to get realistic results. Hold
time, Latency and motion features using accelerometer data were extracted
and the analysis was done using random forest and KNN classifiers. The
accelerometer data provides additional features like mean of all X, Y and Z
axis values.
Chapter5presentsadrugpredictionmethodinhealthcareusingbigdataand
machine learning method. The Health Care System is literally losing patients
xvii

Preface
due to improper diagnosis, accidents and infections in hospitals alone. The
proposed model will act as informative guide for patients and help them for
taking right medicines for the cure of particular disease. In this chapter, the
authors are proposing use of Hadoop Distributed File System for the storage
of medical datasets related to medicinal drugs. MLLib Library of Apache
Spark is to be used for initial data analysis for drug suggestions related to
symptomsgatheredfromparticularuser.Themodelwillanalyzetheprevious
history of patients for any side effects of the drug to be recommended.
Chapter 6 present the analysis of access delay in Ad hoc wireless networks
for multimedia applications. Mobile ad hoc networks are infrastructure
less wireless networks; all nodes can quickly share information without
using any fixed infrastructure like base station or access point. Wireless ad
hoc networks are characterized by frequent topology changes, unreliable
wireless channel, network congestion and resource contention. Multimedia
applications usually are bandwidth hungry with stringent delay, jitter and
loss requirements. Designing ad hoc networks which support multimedia
applications, hence, is considered a hard task. The hidden and exposed
terminal problems are the main which consequently reduces the network
capacity. Hidden and exposed nodes reduce the performance of the wireless
ad hoc networks. Access Delay is the major parameter which is to be taken
under consideration. Due to hidden and exposed terminal problems network
suffers from serious unfairness problem.
Chapter7presentstheoverviewofDeepLearning.Inlastdecade,thedeep
learning techniques have various wings in each area. It has been demanded by
researchersfortheirwork.Thepredictionandanalysisreportcanbegenerated
through Convolution Neural Network using Deep Learning approaches.
In this chapter, we discuss some widely-used deep learning architecture
and their practical applications. Nowadays, in many typical applications of
machine vision there is a tendency to replace classical techniques with deep
learning algorithms. The benefits are valuable on one hand it avoids the need
of specialized handcrafted features extractors and on the other hand, results
are not damaged, moreover they typically get improved.
Chapter 8 describes the architecture, protocols and application of delay
tolerant networks in Vehicular Ad-Hoc Networks. Due to the high mobility
of vehicular nodes in VANETs, there are high chances of partitions in the
network.InsuchasituationtheprotocolsdevelopedforVANETscannotwork
well and an alternative network known as DTN (Delay Tolerant Network)is
capableenoughtodealwithVANETcharacteristics.Thenetworkwhichdoes
not need any immediate data delivery and can wait for time and delivery of
xviii

Preface
dataisknownasDTN.Theconceptofhold&forwardthemessageisexploited
by DTN. In this book chapter, the authors are providing characteristics,
architecture, and applications of Delay Tolerant Vehicular Ad-hoc Networks.
Thetechnology/technicaltermsusedinthebookchapterareexplainedwherever
they appear or at the Key Terminology & Definitions section. Apart from
regular References, additional References are included in the References for
Advance/Further reading for the benefit of advanced readers.
Chapter 9 presents a comprehensive review of digital image classification
techniques. Image classification is a technique to categories an image in
to given classes on the basis of hidden characteristics or features extracted
using image processing. With rapidly growing technology the size of images
is growing. Different categories of images may contain different types of
hidden information such as x-ray, CT scan, MRI, pathologies images, remote
sensing images, satellite images and natural scene image captured via digital
cameras. In this chapter authors have surveyed various articles and books
and summarized image classification techniques. There are supervised
techniques like KNN and SVM, which classify an image into given classes
and unsupervised techniques like K-means and ISODATA for classifying
image into a group of clusters. For big images deep learning networks can be
employed which are fast and efficient and it also computes hidden features
automatically.
Chapter 10 presents an intelligent medical diagnostic system for diabetes.
In this chapter the neuro-fuzzy technique has been used for the diagnosis of
differenttypesofdiabetes.ItdescribesthetriangularandGaussianmembership
functionsandMamdaniandSugenofuzzyexpertsystem.Variousperformance
measures such as: sensitivity, specificity, accuracy, precision is computed
and compared.
CLOSING REMARKS
In conclusion, we would like to sum up here with few lines that, the book is a
small step towards the enhancement of academic research via motivating the
research community and research organizations to think about the impact of
Socialintelligence,networkingprinciplesanditsapplicationsforaugmenting
the academic research. This book is putting insight on the various aspects
of the academic social networking research and need of knowledge sharing
and prediction of relationships through several links and their usages. This
includes the research studies, experiments and literature reviews about social
xix

Preface
networkingactivitiesandtodisseminatecutting-edgeresearchresults,highlight
research challenges and open issues, and promotes further research interest
and activities in identifying missing link in stochastic social networking.
We hope that research scholars, educationalists and students alike will find
significance in this book and continue to use it to expand their perspectives
in the field of Social Networking and its perspective future challenges.
Babita Pandey
Aditya Khamparia
xx

Acknowledgment
Iwouldliketoprecisemygratitudetothemanypeople;thosewhocontributed,
supported and guided me through this book by different means. This book
would not have been possible without their guidance and the help.
First and foremost, I want to express heartfelt gratitude to my Guru for
spiritual empathy and incessant blessings, to all teachers and friends for their
continued guidelines and inspiration throughout the period of my studies and
career. I wish my special gratitude to Dr. Babita Pandey my research guide;
for her blessings and continuous inspiration.
IwouldliketothankIGI-Global,USpublisherwhogavemeanopportunityto
publish with them. I would like to express my appreciation to all contributors
including the accepted chapters’ authors, and many other contributors who
submitted their chapters that cannot be included in the book. Special thanks
to Ms. Mariah Gilbert, Ms. Jan Travers, Ms. Maria Rohde and Ms. Josephine
Dadeboe from IGI-Global –team for their kind support and great efforts in
bringingthebooktocompletion.TheencouragementoftheEditorialAdvisory
Board (EAB) cannot be exaggerated. These are renowned experts who took
timeofftheirbusyschedulestoreviewchapters,provideconstructivefeedback,
and improve the overall quality of chapters.
I would like to thank Dr. R B Mishra, Prof. Sandeep Garg, Prof. Kiran Pandey
and all dear teaching and non-teaching staff-colleagues from our institute -
LPU, Punjab. Special thanks to Dr. Babita Pandey i for motivating me for
this book. Thanks to Prof. Shrikant Tiwari, Dr. Aman Singh, Dr. Devendra
Pandey and Dr. Deepak Gupta for their kind support.
I would like to thank my dear friends Mr. Sanjay Kr. Singh and Mr. Mamoon
Rashid for their continuous support and countless efforts throughout the
process of publication of this book.
xxi

Acknowledgment
IexpressmypersonalandspecialthankstomybelovedfatherKrishnaKumar,
mother Asha, my wife Shrasti, and other family members for supporting me
throughout all my career, for love, the tremendous support and inspiration
which they gave me in all these years.
Last but not the least: I request forgiveness of all those who have been with
me over the course of the years and whose names I have failed to mention.
Aditya Khamparia
xxii

Copyright © 2019, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
Chapter 1
1
DOI: 10.4018/978-1-5225-9096-5.ch001
ABSTRACT
Link prediction in social network has gained momentum with the inception
of machine learning. The social networks are evolving into smart dynamic
networks possessing various relevant information about the user. The
relationship between users can be approximated by evaluation of similarity
between the users. Online social network (OSN) refers to the formulation of
association (relationship/links) between users known as nodes. Evolution of
OSNs such as Facebook, Twitter, Hi-Fi, LinkedIn has provided a momentum
to the growth of such social networks, whereby millions of users are joining it.
The online social network evolution has motivated scientists and researchers
to analyze the data and information of OSN in order to recommend the future
friends. Link prediction is a problem instance of such recommendation
Similarity-Based Indices or
Metrics for Link Prediction
Praveen Kumar Bhanodia
Kamal Kumar Sethi
Acropolis Institute of Technology and Research, India
Aditya Khamparia
https://orcid.org/0000-0001-9019-8230
Babita Pandey
Babasaheb Bhimrao Ambedkar University, India
Shaligram Prajapat
IIPS DAV, India

2
Similarity-Based Indices or Metrics for Link Prediction
INTRODUCTION
The history of evolution of network structures had been studied by several
mathematicians’ long back. Eulars theorem of graph theory was first of its
kind which we can say solved initially the problem of seven bridges given
by Konigsberg (Biggs et. al. 1986). Since then the field of graph theory
and research in this area was handled by mathematicians quite effectively.
Knowledge retrieval and processing techniques now a days are pretty useful
in crunching voluminous data captured via internet (Khamparia & Pandey
2016, 2017). Rule extraction
A social network is a network of people connected with each other
resembling some kind of relationships in between over the internet, in other
words we can say it is typically represents a social structure consists of
social actors having association between these actors. These social networks
are represented through graphs where the actors referred as nodes (users/
individuals/organizations/cities, etc.) and association in between referred as
edgesalsoknownaslinks(relationships/interactions/associations/ties).Earlier
before the inception of internet the communication and cooperation between
people was not convenient and fast but due to rapid development since then
it has become so and the social networks have evolved quite significantly.
The social networks now transformed into online social networks such
as Facebook, Twitter, and LinkdIn, are now became an integrated part of
human life. These (OSNs) online social networks are providing platforms
for exchanging formal and informal information with each other. As a result
of that huge database or voluminous data is getting piled up exponentially.
the data incurred has obvious characteristics and attributes if exploited can
generate useful information for further use to create certain recommendation
system, lot many researchers are now paying attention to social network
analysis for extracting valuable knowledge for better services to the society.
The nature of these kinds of networks is quite dynamic with new edges
and nodes are adding to the graph over the period of time. Comprehending
and understanding the evolution of OSN is typically a complex challenge
due to range of parameters. An instance of social network evolution could
systems. Link prediction is basically a phenomenon through which potential
links between nodes are identified on a network over the period of time. In
this chapter, the authors describe the similarity metrics that further would
be instrumental in recognition of future links between nodes.

3
be easier problem to understand and link prediction (Liben-Nowell and
Kleinberg, 2003) is one such instance where association between nodes is
to be predicted. For example the questions to be answered can be how does
the relationship between nodes changes with respect to time? What could be
the factors affecting this relationship? What kind of influence nearby nodes
can put on the relationship of associated nodes? Ultimately the problem here
in this chapter is an effort to trace out the metrics involved in prediction of
likelihood of future links between nodes.
The Graph
Any problem which is imitated mathematically can be analyzed and solved
using computing facilities even when the scale of the problem is significant
and difficult to understand and comprehend. The size of social networks
is increasing exponentially and so is exploiting the data and information
captured directly and indirectly by these networks. These networks created
online and can be represented through a mathematical structure known as
graph. It has a structured representation having set of vertices (nodes) V
and set of links (or edges) and typically written as G=(V,E). As discussed
above vertices (nodes) represents people and edges or links between them
as relationships between people. edge or link is designated with letter e such
that e belongs to E connecting set of two nodes from V. for example V =
{a, b,c,d,e} and E{e1,e2,e3,e4, where E = ({e1= a,b},{e2=c,d},{e4=a,e}).
In order to illustrate it further it says the graph is collection of five distant
people named as a,b,c,d and e. a and b are friendly with each other, similarly
c-d and a-e. It is illustrated diagrammatically.
Figure 1. Demonstration of nodes and links in graph

4
Sociologist usually call such diagrams as sociograms and in the field
of research domain terms like network, social network, sociogram, graphs
are interchangeable. The links in the network are undirected or bi-directed
which means the exchange of information would be from both sides (ex:
exchange of messages, emails, etc.) . In order to explore the graph theory is
recommended in (Wilson, 1996).
The Link Prediction Problem (Hasan & Zaki 2011)
Let a social network is represented through a undirected and un-weighted
graph G(V,E) at a specific time interval t, where V is the set of nodes and E
referstothesetoflinks/edgesbetweennodes.Linkpredictionisapproximation
of future links between nodes at time t’ where t’>t, or missing links with in
the network.
Let us understand the problem by taking an example of 7 random people,
Asshownbelowin2(aandb)solidlinksbetweennodesshowsexistingedges/
links and relationships between the nodes at time t, dashed links exhibits
probability of new link at the time interval [t,t’]. For example Ashish and
Ajay are friend to each other and a link is displaying association between
these two. The relationship (friend) shown is a feature of link/edge, similar
kind of association can be understood for Ajay and Shri, it is to be noted that
the type of relationship (brother) is different than previous two . There is no
link between Himanshu-Rohit, Ashish-Ashwin and other nodes too initially
(time instance t) but at the next instance (t’=t+1) there would be probability
that some kind of association or relationship occurs and link or edge would
be established (dashed lines) which is to be predicted. Obviously it would be
done by exploiting the available past structural information of the network.
Mathematically in terms of sets it can be understood as:
G(V,E)= Social Network Instance at time instance, V ={u,v,x…n}
e(u,v)ϵE = edge between nodes u and v belongs to set of edges E, showing
interaction or association
G[t0, t1] = Given Subgraph at a timestamp between t0 and t1>t
G[t1,t2]=Subgraph inferring new edges used for testing purpose at a time
stamp t1and t2>t1
Score(xuv
)=score computed between the nodes u and v

5
According to Liben-Nowell and Kleinberg the problem of link prediction
(Liben-Nowell & Kleinberg 2003) has been formulated in three ways with
respect to time.
The problem of link prediction is addressed by various researchers in
differentwayspotentialresearchershavingpotentialknowledgeinmathematics
andphysicsexploitingthestructuralfeatures(nodesandedges)ofthenetwork
whereas data scientists having potential skills in machine learning used to
exploit the node and edge attributes information for the prediction of future
links.
1. Addition of new links: Over the period of time new links will be added
to the existing network
2. Removal of existing links: Over the period of time existing links may
be removed due to noise or otherwise.
3. Addition and Removal of links: At time t+1 new links and exiting links
added and removed simultaneously.
The chapter only discuss about prediction of new links which may appear
in future within the network. The reason for the same is that mostly research
is undergoing over the first type of link prediction and hence we would be
having more data and methods available to exploit and correlate.
Figure 2. (a) Network at time t. (b) Network at time t’=t+1

6
The General Method Adapted for
Approximation of Link Prediction
Prediction of future links by processing the local features of nodes and edges
a heuristic algorithm is used assigning a similarity matrix S containing score
sxy between nodes x and y. This score could be used as a measure or index
of similarity between the nodes. It is worth noting here that every pair of
nodes x,y belongs to set of vertices V (x,y ϵ V) where sxy
=syx
. The computed
score for all the future links would be arranged in descending order, the links
having the top score are most probable to exist in future (Hu, K., Xiang).
As it is obvious in any way we cannot predict the future links in a network,
to verify the accuracy of the link prediction method’s accuracy the sample
networksetisbifurcatedintraining(70%oftheentiredataset)andtestset(30%
of the set), no information from the test set would be used for training the
model. The accuracy of the prediction is evaluated by are under the receiver
operating characteristic curve abbreviated as AUC.
Accuracy of the method can be defined as
AUC n n
= +
( ' . ") /
0 5
Suppose all the score which are generated from independent and identical
distribution, accuracy of the method should be about 0.5. Hence degree by
which accuracy exceeds 0.5 used to shows the performance of the method.
The Application of Link Prediction
ApartfromapplicationofLinkpredictioninsocialnetworksithasmanyother
applications such as useful in finding protein-protein interactions (Airoldi et.
al.2006); E-commerce recommendation systems where suggesting who will
buy what on Flipkart, Amazon is another such kind of application where link
predictionisapplied.Inthesamefashionlinkpredictionhelpsinidentification
of hidden groups or communities of terrorists or criminals. Many researchers
are working on co-authorship networks wherein two researchers who are
close to each other may collaborate and will be colleagues in area of common
interest (Gao & Guan, 2012).

7
The Metric
The values computed from graphs structural features (node degree and
distance) and contributing in description of the graph in some manner is
referred as metric. A metric is typically used by researchers to analyze the
social network which is basically a mathematical formula that computes
the network features. For example degree and common neighbors are such
two metrics generally categorized as monadic and dyadic respectively as
illustrated by Wasserman S. and Foust K. in (Wasserman& Faust1994), all
the traditional social network analysis metrics are summarized by Hanneman
in (Hanneman, R. 2001)). Degree is supposed to be calculated for node, it
is count of nodes connected to node whose degree is to be calculated which
otherwise display the social existence of the node and its popularity in the
social network. Common neighbors value normally calculated for pair of
nodes referred as a dyad. Total number of common neighbors of dyad is
basically count of mutual nodes that two nodes shares. This is illustrated
as how many common friends two persons can have. These two metrics are
basicallycommonneighborhoodbasedmetricswhicharesupposedtoexploit
thenodefeatures(nodeanalysis),moreoverthereareotherneighborhoodbased
metrics in practice such as Jaccaard Coefficient, Adamic Adar, etc described
in later part of the chapter. The other type of metric used is distance(path)
based metric used to involve shortest path computation between the nodes.
For example Katz measure. This chapter is an effort to focus upon the metrics
used for prediction of link in social network.
In order to understand the metrics properly let us explore few graph theory
basics, it can usually be referred on the basis of direction of links of network,
consequently:
Figure 3. Dyad and Triad demonstration

8
1. Metrics for links of bidirectional nature(incoming and outgoing links
both)
2. Metrics for outgoing links
3. Metrics for incoming links
4. Metrics for undirected links
The bi-directed links represents in-degree, out-degree and in-out-degree
for all the types of links. For the node shaded with different color has in
degree of 2, out-degree of 3 and in-out degree 5.
The spectrum of notations and definitions used in these different ways
includessetofshortestpath,recency,distanceandstrengththedetaildescription
of graphical notations is illustrated in figure 5.
These are generally classified into three different categories:
1. Monadic metrics: It is computed over a single node for example node.
It is typically defined for a node ui
at time instance t.
2. Dyadic Metrics: It is computed on pair of nodes for example common
neighbors.Itismostlyusedforapproximationoflinkpredictioninsocial
network.
3. Graph Metrics: This type of metric would be computed over the whole
graph for example what is the size of the graph.
Figure 4. Links and Directions

9
LINK PREDICTION METRICS
Monoadic Metrics
Degree of Node
The degree of a particular node in social network is typically total number
of links it is having connected with other nodes. For example a node is
connected with 5 different distant nodes than the degree of the node would
be 5. In-Degree is the total number of links coming to the node/vertex. Out
Degreeofthenodeisthetotalnumberoflinksleavinganode/vertex.Similarly
In-Out Degree is the total count of incoming and outgoing links/edges. The
significant of degree of a node is such that degree distribution across the
network can be obtained which could be used for further network analysis.
The degree distribution is basically a kind of probability distribution of these
degrees over the entire social network.
Mathematically it can be represented as
Degree (x)=#{{x or #( (x
jj jj i
x Un
: }} ))
∈ Γ
Figure 5. Graph notations used in definition and analysis of the network

10
Degree Centrality
The degree of centrality is most primitive score or measure which says that
a node with higher degree is more central. It determines the total number
of links to a given node in the network. In an undirected graph it could be
a count of links for a node, for directed type of networks it would count of
in-degree and out degree determining the centrality score. The measures
used to answer for social networks that how central a specific node is. In
other words it gives us the most popular node in the network which is having
maximum number of links. Usually centrality score is a kind of asset to any
node of the network as it shows the level of activity and involvement of the
node within the network.
More often in order to normalize or standardize the process of degree
centrality measure as to compare the networks of different and varied sizes,
the score is divided by the maximum possible in-degrees and interpret the
results either by percentage or proportion: (#Г(vi)/#(V)-1). As demonstrated
below the degree centrality distribution in Zachary’s karate social network.
Degree Eccentricity Centrality
It is basically a distance based measure where centrality of the nodes is
measured on the basis of distance between the nodes. It is arguably a simpler
Figure 6. Centrality score for Zachary’s Karate Club Network (Zachary 1977)

11
notion when compared to closeness (Wang et. al. 2015). The eccentricity of
a node in any connected network G is the maximum distance between two
nodes within the network over all nodes of the network G. If the network
is disconnected than the eccentricity for the nodes would be infinite. The
maximum eccentricity of the network or graph is graph diameter (maximum
hops required to reach to a node from other node in a given network) or
network diameter and minimum would be graph radius or network radius
(maximum hops required to reach to central node from any other node within
the network).
Formally it can be stated as:
e v dist u v u V G
g G
( ) : max{ ( , ) : ( )}
= ∈
Generally it has been said that Eccentricity is referred as the reciprocal of
the eccentricity of a node because the reciprocal of the eccentricity value is
quiteeasytocomputesinceitfollowsmonotonicityrule(MatjazKet.al.2018).
Jordan Centrality
Hage and Harary (Hage, P. & Harary, F.,1995) implicitly introduced Jordan
centrality which was derived actually from Jordan center of given network.
Jordancenterofagivennetworkisreferredasthesetofnodeshavingminimum
eccentricity, which means, set of all the nodes across network such that the
greatest distance between nodes u and v, (distu,v
) should be minimal. In other
words we can say that it is the set of nodes having eccentricity equal to the
radius of the network.
Jordan Centrality Cj
formally can be written as:
C
MAXd x y
j
=
1
( , )
where y is not equal to x
Theauthorshavearguedthatidentifyingthenodeswiththehighestcentrality
value would offer worthy insights of a given social network.

12
Closeness Centrality
Closeness centrality yields how close a node to other nodes in a network is,
it is determined by identifying the minimum path distances from the nodes.
A node which is close to other nodes may easily and effectively interact with
them without passing through many intermediaries nodes. In other words if
two nodes are not connected directly then it should at least take minimum
number of hops to reach other node to attain a higher closeness centrality.
Generally it measures the node to node mean path distance, it is worth
mentioning here that geodesic distance is a shortest distance between two
nodes. Then the mean geodesic distance for node v is:
Closeness v
d
i v vi
( ) =
∑ ≠
1
The fartherness of node v is referred as summation of its distance to all
the other nodes and closeness is defined as the inverse of the fartherness.
It is standardized by dividing with the maximum possible value that is 1/
(n-1). If in case of no path possible between node v and i then total count
of vertices would be used in the formula in place of path length. It is to be
noteworthy that more central the node is lower would be the distance to
all other nodes. In a social network closeness centrality has significance in
prediction of links between the nodes as the score calculated would endorse
that the closer node obviously would have probability to have a direct link in
future. The calculated computation of mean distance gives low values for the
nodes situated near to the central nodes and higher values for them situated
far away from central node which is quite opposite to other centrality metrics
thus is not considered as centrality measure with respect to the previous ones.
Therefore research community of the domain usually computer its inverse,
known as closeness centrality.
Betweenness Centrality
The Betweenness centrality measure metric quantifies how many times
a specific node would act as a intermediary node along the shortest path
distance in between two distant nodes. It was introduced by Linten Freeman
to quantify human’s control in an ongoing communication between humans
in a social network. The concept for the measure is such that the node having

13
high probability of occurrence on a random chosen path distance in between
two distantly parted nodes would have a high Betweenness.
The Betweenness centrality for a vertex v in a graph G (V, E) can be:
1. Compute shortest path distance between the pair of nodes(s, t).
2. Determining the fraction of shortest path distance passing through the
nodewhoseBetweennesscentralityistobecalculated(forexamplenode
v)
3. Determining the sum of fraction of all of the pairs of nodes (s,t)
Formally it is represented as
Betweenness v
v
s v t
st
st
( )
( )
= ∑
≠ ≠
σ
σ
The metric can be further normalized or standardized by dividing with
number of pairs of nodes not including v which for directed graph is (n-1)
(n-2) and for undirected graph it is (n-1)(n-2)/2.
PageRank
PageRankalgorithmhasbeenintroducedbyLarryPageco-founderofGoogle
and it is not just because it ranks the pages. According to this algorithm ranks
are assigned to particular web pages and the ranks of the page would be an
average of about 1. Typically the rank is depicted in the range of 1 to 10, 0 is
supposed to be assigned to the least ranked web page and so forth for other
web pages. For examples ranks of some websites are like www.google.com
has 9/10 and www.amazon.com has 8/10. It is an algorithm which is based on
link based object raking problem where the purpose is to assign a numerical
value(Rank)toeachoneofthepageexploitingtheweblinkstructure(Getoor,
L., 2005). PageRank usually counts the number and quality of links to a web
page as to approximate the importance of the website. The main objective
behind is more important web pages of the websites are more likely to have
incoming links from other websites.
The primitives of the algorithm or metric exploit the count and quality
of backlinks or inlinks to specific web page or node. A back link of node P
is a citation to P itself from another node. As demonstrated in above figure
of a network links falling on node E are backlinks for the node and links

14
leaving the node are called as outlinks. Node A and node C are having single
backlinks, similarly node B and node D are having two backlinks, and same
way 3 backlinks are falling upon node E. As per the illustration of pagerank
algorithm node E is found to be more potential and significant relative to
other four nodes. Along with counts the measure also considers the quality of
backlinks for setting up the priority value in order to make the method more
reliable and accurate. Thus backlinks from node E will hold more importance
than a backlink from node A. Node B is having higher rank than D since it
is having back links from D and E.
Ranking of nodes in a given social network is not easy because the social
networkonwhichthemethodissupposedtobeappliedhasrelevantchallenges
like social networks are of dynamic nature, the frequency with which nodes
of the network exchange information changes readily, the number of links
of a particular node in the network will increase or decrease with respect to
time and availability of relevant data and information. Moreover the major
disadvantage with the simple approach is that the reliability of backlink
cannot be trusted because there are fair chances that one can create fake
reviews and spams as to increase the backlink counts. In order to overcome
such spams, ranking of nodes generating backlinks will also be considered
and the repetitive process so created makes it more reliable and accurate.
Figure 7. Social network

15
In order to formally define PageRank we will summarize the essential
terminologies and notation used in defining PageRank mathematically
(Figure 8).
As per illustration to compute rank of a node in a social network, suppose
P1
, we have to see at all the other nodes which are linked to P1
that is having
backlinks to P1
. Let us say P2
is a node having three outlinks (outgoing links
to other nodes) in addition to one link going to P1
. the contribution of P2
to
P1
in terms of rank would be 1/4th of its PageRank. The total of P1
the
summation of all values of nodes linked to it has to be obtained. In general
if the node Pv
is having n links to other nodes {Pu
| u ϵ 1,2,3……n}, in this
case the contribution of Pv
will be only
1
deg( )
Pv
th of the links it is having
to the PageRank of node Pu
and it can be written as:
PR P
PR Pv
Pv
u
( )
( )
deg( )
= ∑ +
Applying the formula to get the PageRank of node B
Figure 8. Symbols and notation for PageRank Algorithm

16
PR B
PR E PR D
( )
( ) ( )
= +
2 2
In the same fashion we can find the PageRank for all the nodes across the
socialnetwork.ForeachnodePv
wehavetodetermingthenumberofoutgoing
links of Pv
(deg(Pv
)+
) and its PageRank PR(Pv
). for every node Pv
first we
have to determine the ratio of its calculated PageRank for the corresponding
outgoing links count and then computing the sum over all of the nodes which
are linked to a specific node of interest. Formally for the PageRank of P it
can be defined as [15] (Brin, S., and L. Page.,(1998).
PR P d d
PR P
P
PR P
P
PR P
P
( ) ( ) (
( )
deg( )
( )
deg( )
( )
deg( )
= − =
+
+
+
+ +
1 1
2
2
2
3
3
⋅
⋅⋅⋅⋅⋅⋅ +
+
PR P
P
n
n
( )
deg( )
where d is the damping factor which is used for representing a factor where
the user is getting bored while browsing the web page and about to open a
new web page. Typically the value for damping factor d is 0.85.Vice versa
(1-d) would be the probability for the user not getting bored and will remain
on the web page.
Dyadic Common Neighbor Based Metrics
Common Neighborhood
The CN is determined on the basis of number of common neighbors existing
between two nodes where future link is to be predicted. The application of
this approach was initiated on collaboration networks by Newman (M. E. J.
Newman2001).Itprovidesalinkpredictionscoreforsimilaritybycalculating
theintersectionofthesetsofneighborsofthenodestopredictexistencefuture
link. As shown the nodes are the network entities (users, items, etc) and the
edges representing the relationship between users. The dotted line represents
future relationship/link which is to be predicted while solid lines are existing
relationships. The Common Neighbors (CN) is calculated as follows:
Common Neighbors (CN x y x y
( , )) ( ) ( )
= ∩
Γ Γ

17
where Γ(x) = (number of common neighbors to x) and Γ(y) = (number of
common neighbors to y)
As demonstrated in Figure 4, common neighbors of node A and node C
that is CN (AC) = 1 and common neighbors between node F and node H is
1 thus the score between both pairs of node is 1 (CN (AC) = 1) and CN (FG)
= 1). Likewise the score for all the non existing links of the social network at
a time instance t is computed and sorted in an order. Links with high score
have more probability to exist at t+1 time instance.
MoreovertheweightedCommonNeighbors(CNw
)wouldbedeterminedas
follows where w(x,y)
is the number of interactions between the nodes x and y.
CN
w x z w y z
w x y
ze x y
( , )
( )
( , ) ( , )
=
+












∩ ( )
∞
Γ
Σ 2
Jaccard Coefficient
Itisanothersimplemetricconsideredforlinkpredictionwhichisanormalized
formofcommonneighborhoodtechnique,becauseitalsoconsiderstheunion
of common neighbors of the two nodes between which future links is to be
predicted. Thus the probability of predicting a link between nodes can be
approximated by score obtained using formula given below:
Figure 9. Common Neighborhood & Jaccard coefficient demonstration

18
JC
x y
x y
xy
=
∩
∪
Γ Γ
Γ Γ
( ) ( )
( ) ( )
Example: According to Jaccard Coefficient (JC) the score for prediction
of a link between nodes AC (refer figure-4) would be JC (AC) = 1/6 = .166 .
Similarly score for link between node F and node G would be JC (FG) =
½ = 0.50. Hence probability of node F and node G to be linked at time t+1
instance is more than linking of node A and node C.
Adamic/Adar
According to Adamic and Adar the metric is designed to develop to consider
the common neighbors between nodes which are not connected directly.
Basically it considers all the common neighbors (common friend) existing
between nodes and the number of nodes (degree of the node) connected
to each common neighbor is also considered for computation of the score
(Adamic and Adar 2003). Thus the probability of being a connection between
the nodes of social network is determined by
AAxy
z
ze x y
=
∩
∞
∑
1
log ( )
( ) ( ) Γ
Γ
where z is the set of common neighbors of nodes x and y
As shown in Figure 10 where dashed lines represent the future links while
solid represents the existing links. The score between nodes A and C is AA
(AC) = 1/log4 + 1/log2. Similarly the score for other links like AA (EF) is
1/log4 and AA (GH) is 1/log 5. Therefore if a neighbor node has more links
better score or index value would be obtained.
Resource Allocation
The measures discussed above are usually neighboring node based, this
measuring metric is basically based on resource allocation process that
happens in networks. The approach considers nodes x and y which are not
connected directly, suppose node x sends some kind of resource (message or
data) to next node y via common neighbors used to play role of transmitters.
it is assumed that these common nodes (so called transmitters) will have a

19
unit of information and distribute it equally between all of its neighbors here
the similarity can be identified between the nodes by the score determined
using the equation given below (Zhou & Zhang 2009).
RA
N Z
xy
ze x y
=
∩
∞
∑
1
( )
( ) ( )
Γ
It is noteworthy that index score sxy
= syx
, accordingly refer figure, here
the resource allocation score value between nodes A and C is determined as
RA (AC) = 1/3 +1/3 = 2/3 = .66, similarly the score value between nodes G
and H would be RA (GH) = 1/3 = .33. The probability of happening a link in
near future between nodes A and C is more than nodes G and G. In the same
fashion research allocation index score for non existing links between the
nodes across the entire social network would be determined and the resultant
score is sorted and arranged.
Salton index
This index was proposed by G. Salton and defined as the ratio between the
common neighbor node and the square root of product of degree of node x
and node y for which link has to be predicted in near future. Formally the
equation for the metric can be written as:
Figure 10. Adamic/Adar Demonstration

20
S
x y
k x k y
xy
=
( )∩ ( )
√ ( )× ( )
Γ Γ
where k(x) =|Γ (x) |denotes the degree of x. Salton index is also called cosine
similarity in the available literature (Srilatha and Manjula 2016).
Preferential Attachment (PA)
According to Jérôme Kunegis et. al. (Kunegis et. al. 2013) the approach
claimsthattheprobabilityofestablishinglinkbetweennodesdependsonhow
potential a node is. It says that node x having high degree than node y will
attract new neighbor nodes faster towards it. Figure demonstrates that since
the node degree of node A in the network is 5 and at the same time degree
of G is 3, therefore the link prediction probability for AC is more than GH.
Mathematically it can be defined as
PA x y
x y
,
.
( )
= ( ) ( )
Γ Γ
According to the formula discussed above the score for preferential
attachment for PA(AC) would be 5* 2 = 10 and PA(GH) = 3 * 2 = 6, hence
Figure 11. Demonstrating Resource allocation metric

21
nodes A and C has higher probability to be connected in future rather than
nodes G and H.
Sørensen Index
This index is mainly used for ecological community data (Sørensen 1948,
Zou et. al. 2009) which is defined as
S
x y
k x k y
xy
=
( )∩ ( )
( )+ ( )
2 * Γ Γ
Hub Promoted Index (HPI)
The metric is introduced to deduce the structural overlapping of substrates
pairs in complex networks. The approach defines the ratio of common
neighbor nodes between node pairs to the minimum total number of node
connected to the node among the node pairs (whichever is minimum x or
y). According to Barabasi et. al.(Ravasz et. al.)the metric links connected
to the hub node (node with very large degree) will be assigned with higher
scores as the denominator with respect to the equation is of low degree only.
Figure 12. Preferential Attachment Demonstration

22
S
x y
k x k y
xy

2*
min ,

Hub Depressed Index (HDI)
ThemetricisjustanaloguestoHPI,wheredenominatorisreplacedwithdegree
of the node linked with maximum adjacent node. The metric is supposed to
produce the opposite effect than nodes having maximum degree. The metric
can be defined as
S
x y
k x k y
xy
=
( )∩ ( )
( ) ( )
2 *
max ,
Γ Γ
Leicht–Holme–Newman Index (LHN)
AccordingtoLeichtet.al.(Leichtet.al.2006)themetricproposedastodefine
a measure exploiting local topological similarity index. The approach is a
ratiobetweencommonadjacent(neighbor)nodes(x,y)andthemultiplication
of node x y degrees. LHN thus written as
S
x y
k x k y
xy
=
( )∩ ( )
( ) ( )
2 *
* |
Γ Γ
The value of the metric determined for x-y would be same for y-x as well.
ItwouldbenoteworthythatvaluecalculatedusingSaltonindex/metricdiffers
from LHN as the denominator of both the metrics is different. Salton will
always yield a higher value than LHN for the same set of inputs.
Path Based Feature Metrics
These metrics are usually also known as global similarity method that uses all
information on network to calculate the similarity matrix between two nodes,
the hops between the two nodes to recognize the closeness and similarity
will be 2.

23
Path Distance
Distance between nodes in a graph is one obvious measure to recognize the
closeness of two nodes, also known as geodesic distance. Applying Dijkstra’s
algorithm for extracting the shortest path would be inefficient between two
nodes in a social network rather it can be exploited with a small real world
property of the social network by applying expanded ring search. It will
compute the (negative) shortest path distance between two nodes. A score
calculated is analyzed based on which future link would be predicted between
two nodes having shortest path.
Use of negative signed shortest path shows that proximity for GDxy
increases with the closeness of nodes x y. As shown in above figure 7 the
path score for AC is -3, score for AE is -2 and score for GH is -4. According
to the path distance calculated where AE ACGH, thus nodes A and E are
more likely to be connected in future compared to other nodes.
Katz(Exponentially Damp Path Counts)
A measurement that takes all paths between two nodes in consideration while
rating short paths more heavily. The measurement exponentially reduces the
Figure 13. Path Distance

24
contribution of a path to the metric in order to give less weight to longer
paths. Therefore it uses a factor of βl
where l is the path length.
Katz xy
( )= ( )
=
∑
l
n
path x y
0
² ,
The β can be used to control how much the length of the paths should be
considered. A very small β concludes to an algorithm where paths of length
three or more are taken much less into account and therefore the algorithm
converge the node neighborhood algorithms. It has roughly has a cubic
complexity as it requires matrix inversion (Wang et. al. 2015).
Measurement Index in Weighted Networks
The link prediction methods in weighted networks are: Weighted common
neighbor (WCN), Weighted Adamic/Adar (WAA) and Weighted Resource
Allocation (WRA).
Weighted Common Neighbor (WCN)
S w x y w z y
xy
WCN
z Oxy
= ( ) + ( )
∈
∑ , ,
α α
Weighted Adamic/Adar (WAA)
S
w x y w z y
s z
xy
WAA
z Oxy
=
( ) + ( )
+ ( )
( )
∈
∑
( , , )
log
α α
1
Weighted resource allocation (WRA)
S
w x y w z y
s z
xy
WRA
z Oxy
=
( ) + ( )
( )
∈
∑
( , , )
α α

25
Where Oxy is the set of common neighbours of node pair (x,y), w(x,z) is
the weight of the link between ,

S x w x y
z x
( )= ( )
∈ ( )
∑
Γ
α
x and z, and. Moreover,
when α = 0, the s(x) is the degree of node x, and the indices degenerate to
the unweighted cases. When α=1, the indices are equivalent to the simply
weighted indices. Generally, the optimal values of α are smaller than 1in
most of the weighted networks.
DISCUSSION
Link prediction metrics or methods in social network are typically used to
computeascoreknownassimilarityscorebaseduponcommonneighborhood
friends or nodes. The metric obtained helps in knowing the future links
between the nodes within the structure. it is quite noteworthy that the local
structure based metrics is computed between the nodes where the path length
is maximum of 2. In case of global structure this path length may vary as we
traverse the nodes to reach a specific node from a node. The disadvantage of
local structure could be that there is possibility of important and potential
links could be missed. Exploitation of entire network to compute measures
is also time consuming. According to methods based on global structure of
the network graph, it has an advantage of exploiting the links missing during
local structure based methods. Exploitation of entire network using global
structure methods could be time consuming particularly in the case of large
and complex social networks as the data and information of such network
is of Petabytes.
Thus there is a huge scope of development for scalable local and global
structurebasedmetricsormethodswhichcanincludeallthemissingpotential
links and also consumes less time for crunching of large social networks.
There are hybrid methods considering both the methods into consideration
also known as quasi-local structure based methods predicting missing or
future links appears to be more precise and accurate than each one of these
two.Exploringensembletechniqueforsocialnetworkanalysisandprediction
of missing or future links between nodes accurately and efficiently could be
an interesting exercise to work upon.

26
All the methods discussed above have been proposed are exploiting the
local and global topological structure of the network, community features
withinthenetworkisnottakenintoconsiderationforcomputationofsimilarity
score values. There is a strong probability that use of such information will
goingtoimprovetheaccuracyofpredictionoflinks.Hopcraftandsoundrajan
(Soundarajan Hopcroft 2012) for RA and CN have shown sustainability in
this direction but the metrics is usually not applied over milestone datasets
and it will obviously be an interesting challenge to be explored. The summary
of discussed metrics along with their complexities is shown in Table (Gao et.
al. 2015). Moreover various other datamining and data retrieval techniques
(Khamparia Pandey 2015, 2018) are needed to be explored to retrieve
relevant information which may further contribute in prediction of potential
links.Rule extraction techniques for information retrieval (Sethi et. al., 2012)
can also be explored for links prediction in social network analysis.
CONCLUSION
In this chapter we have put in an effort to simplify the classical metrics based
on degree of the nodes used for link prediction in social networks. The pool
of metrics is not limited to the discussion made above but there are various
other methods have been proposed by authors based on machine learning
concepts, these methods are out of the scope of the chapter. The chapter
provides a necessary insight to the research newbie’s to develop conceptual
fundamentals regarding online social networks.
Figure14.Summaryofsimilaritybasedlinkpredictionmetricswiththeircomplexities

27
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Exploring the Variety of Random
Documents with Different Content

“Then you approve of concealment!” I exclaimed.
“It is better than open effrontery, it shows that the moral power
in society is the stronger; that it is making the way of the
transgressor hard, driving him into dark corners.”
I contrasted this in my mind with Elodia’s theory on the same
subject. The two differed, but there was a certain harmony after all.
Severnius added, apropos of what had gone before, “It does not
seem fair to me that one half of humanity should hang upon the
skirts of the other half; it is better that we should go hand in hand,
even though our progress is slow.”
“But that cannot be,” I returned; “there are always some that
must bear the burden while others drag behind.”
“O, certainly; that is quite natural and right,” he assented. “The
strong should help the weak. What I mean is that we should not
throw the burden upon any particular class, or allow to any
particular class special indulgences. That—pardon me!—is the fault I
find with your civilization; you make your women the chancellors of
virtue, and claim for your sex the privilege of being virtuous or not,
as you choose.” He smiled as he added, “Do you know, your loyalty
and tender devotion to individual women, and your antagonistic
attitude toward women in general—on the moral plane—presents
the most singular contrast to my mind!”
“No doubt,” I said; “it is a standing joke with us. We are better
in the sample than in the whole piece. As individuals, we are
woman’s devoted slaves, and lovers, and worshipers; as a political
body, we are her masters, from whom she wins grudging
concessions; as a social factor, we refuse her dictation.”
I was not in a mood to discuss the matter further. I was sick at
heart and angry,—not so much with Elodia as with the conditions
that had made her what she was, a woman perfect in every other
respect, but devoid of the one supreme thing,—the sense of virtue.
She was now to me simply a splendid ruin, a temple without
holiness. I went up to my room and spent the night plunged in the
deepest sadness I had ever known. When one is suffering an

insupportable agony, he catches at the flimsiest delusions for
momentary relief. He says to himself, “My friend is not dead!” “My
beloved is not false!” So I tried to cheat myself. I argued, “Why, this
is only a matter of education with me, surely; how many women,
with finer instincts than mine, have loved and married men of
exactly the same stamp as Elodia!” But I put away the thought with
a shudder, feeling that it would be a far more dreadful thing to relax
my principles and to renounce my faith in woman’s purity than to
sacrifice my love. The tempter came in another form. Suppose she
should repent? But my soul revolted. No, no; Jesus might pardon a
Magdalene, but I could not. Elodia was dead; Elodia had never been!
That night I buried her; I said I would never look upon her face
again. But the morning brought resurrection. How hard a thing it is
to destroy love!

Chapter 9.
JOURNEYING UPWARD.
“The old order changeth, giving place to the new,
And God fulfils himself in many ways.”
—Tennyson.
My conversation with Elodia had the effect of crystallizing my
nebulous plans about visiting the Caskians into a sudden resolve. I
could not remain longer in her presence without pain to myself; and,
to tell the truth, I dreaded lest her astounding lack of the moral
sense—which should be the foundation stone of woman’s character
—would eventually dull my own. Men are notoriously weak where
women are concerned—the women they worship.
As soon as I had communicated with the Caskians and learned
that they were still anticipating my coming, with—they were so kind
as to say it—the greatest pleasure, I prepared to set forth.
In the meantime, an event occurred which further illustrated the
social conditions in Paleveria. Claris, the wife of Massilla, died very
suddenly, and I was astonished at the tremendous sensation the
circumstance occasioned throughout the city. It seemed to me that
the only respect it was possible to pay to the memory of such a
woman must be that which is expressed in absolute silence,—even
charity could not be expected to do more than keep silent. But I was
mistaken, Claris had been a woman of distinction, in many ways; she
was beautiful, rich, and talented, and she had wielded an influence
in public and social affairs. Immediately, the various periodicals in
Thursia, and in neighboring cities, flaunted lengthy eulogistic
obituaries headed with more or less well executed portraits of the
deceased. It seemed as if the authors of these effusions must have
run through dictionaries of complimentary terms, which they culled
lavishly and inserted among the acts and facts of her life with a kind

of journalistic sleight-of-hand. And private comment took its cue
from these authorities. It was said that she was a woman of noble
traits, and pretty anecdotes were told of her, illustrating her
generous impulses, her wit, her positiveness. She had had great
personal magnetism, many had loved her, many had also feared her,
for her tongue could cut like a sword. It was stated that her children
had worshiped her, and that her death had prostrated her husband
with grief. Of the chief blackness of her character none spoke.
Severnius invited me to attend the funeral obsequies which took
place in the Auroras’ Temple, where the embalmed body lay in state;
with incense burning and innumerable candles casting their pallid
light upon the bier. I observed as we drove through the streets that
the closed doors of all the business houses exhibited the emblems of
respect and sorrow.
The Auroras were assembled in great numbers, having come
from distant parts of the country to do honor to the dead. They were
in full regalia, with mourning badges, and carried inverted torches.
The religious ceremonies and mystic rites of the Order were
elaborate and impressive. The dirge which followed, and during
which the members of the Order formed in procession and began a
slow march, was so unutterably and profoundly sad that I could not
keep back the tears. A little sobbing voice directly in front of me
wailed out “Mamma! Mamma!” A woman stooped down and
whispered, “Do you want to go up and kiss Mamma ‘good-by’ before
they take her away?” But the child shrank back, afraid of the pomp
and ghostly magnificence surrounding the dead form.
Elodia was of course the chief figure in the procession, and she
bore herself with a grave and solemn dignity in keeping with the
ceremonies. The sight of her beautiful face, with its subdued but
lofty expression, was more than I could bear. I leaned forward and
dropped my face in my hands, and let the sorrow-laden requiem
rack my soul with its sweet torture as it would.
That was my last day in Thursia.
I had at first thought of taking my aeroplane along with me,
reflecting that I might better begin my homeward flight from some

mountain top in Caskia; but Severnius would not hear of that.
“No indeed!” said he, “you must return to us again. I wish to get
ready a budget for you to carry back to your astronomers, which I
think will be of value to them, as I shall make a complete map of the
heavens as they appear to us. Then we shall be eager to hear about
your visit. And besides, we want to see you again on the ground of
friendship, the strongest reason of all!”
“You are too kind!” I responded with much feeling. I knew that
he was as sincere as he was polite. This was at the last moment,
and Elodia was present to bid me “good-by.” She seconded her
brother’s invitation,—“O, yes, of course you must come back!” and
turned the whole power of her beautiful face upon me, and for the
first time gave me her hand. I had coveted it a hundred times as it
lay lissome and white in her lap. I clasped it, palm to palm. It was as
smooth as satin, and not moist,—I dislike a moist hand. I felt that up
to that moment I had always undervalued the sense of touch,—it
was the finest of all the senses! No music, no work of art, no
wondrous scene, had ever so thrilled me and set my nerves a-quiver,
as did the delicate, firm pressure of those magic fingers. The
remembrance of it made my blood tingle as I went on my long
journey from Thursia to Lunismar.
It was a long journey in miles, though not in time, we traveled
like the wind.
Both Clytia and Calypso were at the station to meet me, with
their two children, Freya and Eurydice. I learned that nearly all
Caskians are named after the planetoids or other heavenly bodies,—
a very appropriate thing, since they live so near the stars!
My heart went out to the children the moment my eyes fell
upon their faces.
They were as beautiful as Raphael’s cherubs, you could not look
upon them without thrills of delight. They were two perfect buds of
the highest development humanity has ever attained to,—so far as
we know. I felt that it was a wonderful thing to know that in these
lovely forms there lurked no germs of evil, over their sweet heads
there hung no Adam’s curse! They were seated in a pretty pony

carriage, with a white canopy top lined with blue silk. Freya held the
lines. It appeared that Eurydice had driven down and he was to
drive back. The father and mother were on foot. They explained that
it was difficult to drive anything but the little carriage up the steep
path to their home on the hillside, half a mile distant.
“Who would wish for any other means of locomotion than
nature has given him, in a country where the buoyant air makes
walking a luxury!” I cried, stretching my legs and filling my lungs,
with an unwonted sense of freedom and power.
I had become accustomed to the atmosphere of Paleveria, but
here I had the same sensations I had experienced when I first
landed there.
“If you would rather, you may take my place, sir?” said the not
much more than knee-high Freya, ready to relinquish the lines. I felt
disposed to laugh, but not so the wise parents.
“The little ponies could not draw our friend up the hill, he is too
heavy,” explained Clytia.
“Thank you, my little man, all the same!” I added.
It was midsummer in Paleveria, but here I observed everything
had the newness and delightful freshness of spring. A busy, bustling,
joyous, tuneful spring. The grass was green and succulent; the sap
was in the trees and their bark was sleek and glossy, their leaves
just unrolled. Of the wild fruit trees, every branch and twig was
loaded with eager buds crowding upon each other as the heads of
children crowd at a cottage window when one goes by. Every thicket
was full of bird life and music. I heard the roar of a waterfall in the
distance, and Calypso told me that a mighty river, the Eudosa,
gathered from a hundred mountain streams, was compressed into a
deep gorge or canyon and fell in a succession of cataracts just below
the city, and finally spread out into a lovely lake, which was a
wonder in its way, being many fathoms deep and as transparent as
the atmosphere.
We paused to listen,—the children also.

“How loud it is to-day, Mamma,” exclaimed Freya. His mother
assented and turned to me with a smile. “The falls of Eudosa
constitute a large part of our life up here,” she said; “we note all its
moods, which are many. Sometimes it is drowsy, and purrs and
murmurs; again it is merry, and sings; or it is sublime, and rises to a
thunderous roar. Always it is sound. Do you know, my ears ached
with the silence when I was down in Paleveria!”
I have said Clytia’s eyes were black; it was not an opaque
blackness, you could look through them down into her soul. I likened
them in my mind to the waters of the Eudosa which Calypso had just
described.
Every moment something new attracted our attention and the
brief journey was full of incident; the children were especially alive
to the small happenings about us, and I never before took such an
interest in what I should have called insignificant things. Sometimes
the conversation between my two friends and myself rose above the
understanding of the little ones, but they were never ignored,—nor
were they obtrusive; they seemed to know just where to fit their
little questions and remarks into the talk. It was quite wonderful. I
understood, of course, that the children had been brought down to
meet me in order that I might make their acquaintance immediately
and establish my relations with them, since I was to be for some
time a member of the household. They had their small interests
apart from their elders—carefully guarded by their elders—as
children should have; but whenever they were permitted to be with
us, they were of us. They were never allowed to feel that loneliness
in a crowd which is the most desolate loneliness in the world. Clytia
especially had the art of enveloping them in her sympathy, though
her intellectual faculties were employed elsewhere. And how they
loved her! I have seen nothing like it upon the Earth.
Perhaps I adapt myself with unusual readiness to new
environments, and assimilate more easily with new persons than
most people do. I had, as you know, left Paleveria with deep
reluctance, under compulsion of my will—moved by my better
judgment; and throughout my journey I had deliberately steeped

myself in sweet and bitter memories of my life there, to the
exclusion of much that might have been interesting and instructive
to me on the way,—a foolish and childish thing to have done. And
now, suddenly, Paleveria dropped from me like a garment. Some
moral power in these new friends, and perhaps in this city of
Lunismar,—a power I could feel but could not define,—raised me to
a different, unmistakably a higher, plane. I felt the change as one
feels the change from underground to the upper air.
We first walked a little way through the city, which quite filled
the valley and crept up onto the hillsides, here and there.
Each building stood alone, with a little space of ground around
it, upon which grass and flowers and shrubbery grew, and often
trees. Each such space bore evidence that it was as tenderly and
scrupulously tended as a Japanese garden.
It was the cleanest city I ever saw; there was not an unsightly
place, not a single darksome alley or lurking place for vice, no
huddling together of miserable tenements. I remarked upon this and
Calypso explained:
“Our towns used to be compact, but since electricity has
annihilated distance we have spread ourselves out. We have plenty
of ground for our population, enough to give a generous slice all
round. Lunismar really extends through three valleys.”
Crystal streams trickled down from the mountains and were
utilized for practical and æsthetic purposes. Small parks, exquisitely
pretty, were very numerous, and in them the sparkling water was
made to play curious pranks. Each of these spots was an ideal
resting place, and I saw many elderly people enjoying them,—people
whom I took to be from sixty to seventy years of age, but who, I
was astonished to learn, were all upwards of a hundred. Perfect
health and longevity are among the rewards of right living practiced
from generation to generation. The forms of these old people were
erect and their faces were beautiful in intelligence and sweetness of
expression.
I remarked, apropos of the general beauty and elegance of the
buildings we passed:

“This must be the fine quarter of Lunismar.”
“No, not especially,” returned Calypso, “it is about the same all
over.”
“Is it possible! then you must all be rich?” said I.
“We have no very poor,” he replied, “though of course some
have larger possessions than others. We have tried, several times in
the history of our race, to equalize the wealth of the country, but the
experiment has always failed, human nature varies so much.”
“What, even here?” I asked.
“What do you mean?” said he.
“Why, I understand that you Caskians have attained to a most
perfect state of development and culture, and—” I hesitated and he
smiled.
“And you think the process eliminates individual traits?” he
inquired.
Clytia laughingly added:
“I hope, sir, you did not expect to find us all exactly alike, that
would be too tame!”
“You compliment me most highly,” said Calypso, seriously, “but
we must not permit you to suppose that we regard our
‘development’ as anywhere near perfect, In fact, the farther we
advance, the greater, and the grander, appears the excellence to
which we have not yet attained. Though it would be false modesty—
and a disrespect to our ancestors—not to admit that we are
conscious of having made some progress, as a race. We know what
our beginnings were, and what we now are.”
After a moment he went on:
“I suppose the principle of differentiation, as we observe it in
plant and animal life, is the same in all life, not only physical, but
intellectual, moral, spiritual. Cultivation, though it softens salient
traits and peculiarities, may develop infinite variety in every kind and
species.”

I understood this better later on, after I had met a greater
number of people, and after my perceptions had become more
delicate and acute,—or when a kind of initiatory experience had
taught me how to see and to value excellence.
A few years ago a border of nasturtiums exhibited no more than
a single color tone, the pumpkin yellow; and a bed of pansies
resembled a patch of purple heather. Observe now the chromatic
variety and beauty produced by intelligent horticulture! A group of
commonplace people—moderately disciplined by culture—might be
compared to the pansies and nasturtiums of our early recollection,
and a group of these highly refined Caskians to the delicious flowers
abloom in modern gardens.
We crave variety in people, as we crave condiments in food. For
me, this craving was never so satisfied—and at the same time so
thoroughly stimulated—as in Caskian society, which had a spiciness
of flavor impossible to describe.
Formality was disarmed by perfect breeding, there was nothing
that you could call “manner.” The delicate faculty of intuition
produced harmony. I never knew a single instance in which the
social atmosphere was disagreeably jarred,—a common enough
occurrence where we depend upon the machinery of social order
rather than upon the vital principle of good conduct.
I inquired of Calypso, as we walked along, the sources of the
people’s wealth. He replied that the mountains were full of it. There
were minerals and precious stones, and metals in great abundance;
and all the ores were manufactured in the vicinity of the mines
before being shipped to the lower countries and exchanged for
vegetable products.
This prompted me to ask the familiar question:
“And how do you manage the labor problem?” He did not
understand me until after I had explained about our difficulties in
that line. And then he informed me that most of the people who
worked in mines and factories had vested interests in them.

“Physical labor, however,” he added, “is reduced to the
minimum; machinery has taken the place of muscle.”
“And thrown an army of workers out of employment and the
means of living, I suppose?” I rejoined, taking it for granted that the
small share-holders had been squeezed out, as well as the small
operators.
“O, no, indeed,” he returned, in surprise. “It has simply given
them more leisure. Everybody now enjoys the luxury of spare time,
and may devote his energies to the service of other than merely
physical needs.” He smiled as he went on, “This labor problem the
Creator gave us was a knotty one, wasn’t it? But what a tremendous
satisfaction there is in the thought—and in the fact—that we have
solved it.”
I was in the dark now, and waited for him to go on.
“To labor incessantly, to strain the muscles, fret the mind, and
weary the soul, and to shorten the life, all for the sake of supplying
the wants of the body, and nothing more, is, I think, an
inconceivable hardship. And to have invoked the forces of the
insensate elements and laid our burdens upon them, is a glorious
triumph.”
“Yes, if all men are profited by it,” I returned doubtfully.
“They are, of course,” said he, “at least with us. I was shocked
to find it quite different in Paleveria. There, it seemed to me,
machinery—which has been such a boon to the laborers here—has
been utilized simply and solely to increase the wealth of the rich. I
saw a good many people who looked as though they were on the
brink of starvation.”
“I don’t see how you manage it otherwise,” I confessed.
“It belongs to the history of past generations,” he replied.
“Perhaps the hardest struggle our progenitors had was to conquer
the lusts of the flesh,—of which the greed of wealth is doubtless the
greatest. They began to realize, generations ago, that Mars was rich
enough to maintain all his children in comfort and even luxury,—that
none need hunger, or thirst, or go naked or houseless, and that

more than this was vanity and vain-glory. And just as they, with
intense assiduity, sought out and cultivated nature’s resources—for
the reduction of labor and the increase of wealth—so they sought
out and cultivated within themselves corresponding resources, those
fit to meet the new era of material prosperity; namely, generosity
and brotherly love.”
“Then you really and truly practice what you preach!” said I,
with scant politeness, and I hastened to add, “Severnius told me
that you recognize the trinity in human nature. Well, we do, too,
upon the Earth, but the Three have hardly an equal chance! We
preach the doctrine considerably more than we practice it.”
“I understand that you are a highly intellectual people,”
remarked Calypso, courteously.
“Yes, I suppose we are,” said I; “our achievements in that line
are nothing to be ashamed of. And,” I added, remembering some
felicitous sensations of my own, “there is no greater delight than the
travail of intellect which brings forth great ideas.”
“Pardon me!” he returned, “the travail of soul which brings forth
a great love—a love willing to share equally with others the fruits of
intellectual triumph—is, to my mind, infinitely greater.”
We had reached the terrace, or little plateau, on which my
friends’ house stood; it was like a strip of green velvet for color and
smoothness.
The house was built of rough gray stone which showed silver
glintings in the sun. Here and there, delicate vines clung to the
walls. There was a carriage porch—into which the children drove—
and windows jutting out into the light, and many verandas and little
balconies, that seemed to give the place a friendly and hospitable
air. Above there was a spacious observatory, in which was mounted
a very fine telescope that must have cost a fortune,—though my
friends were not enormously rich, as I had learned from Severnius.
But these people do not regard the expenditure of even very large
sums of money for the means of the best instruction and the best
pleasures as extravagance, if no one suffers in consequence. I
cannot go into their economic system very extensively here, but I

may say that it provides primarily that all shall share bountifully in
the general good; and after that, individuals may gratify their
respective tastes—or rather, satisfy their higher needs; for their
tastes are never fanciful, but always real—as they can afford.
I do not mean that this is a written law, a formal edict, to be
evaded by such cunning devices as we know in our land, or at best
loosely construed; nor is it a mere sentiment preached from pulpits
and glorified in literature,—a beautiful but impracticable conception!
It is purely a moral law, and being such it is a vital principle in each
individual consciousness.
The telescope was Calypso’s dearest possession, but I never
doubted his willingness to give it up, if there should come a time
when the keeping of it would be the slightest infringement of this
law. I may add that in all the time I spent in Caskia, I never saw a
man, woman, or child, but whose delight in any possession would
have been marred by the knowledge that his, or her, gratification
meant another’s bitter deprivation. The question between Thou and
I was always settled in favor of Thou. And no barriers of race,
nationality, birth, or position, affected this universal principle.
I made a discovery in relation to the Caskians which would have
surprised and disappointed me under most circumstances; they had
no imagination, and they were not given to emotional excitation.
Their minds touched nothing but what was real. But mark this: Their
real was our highest ideal. The moral world was to them a real
world; the spiritual world was to them a real world. They had no
need of imagery. And they were never carried away by floods of
feeling, for they were always up to their highest level,—I mean in
the matter of kindness and sympathy and love. Moreover, their
intellectual perceptions were so clear, and the mysteries of nature
were unrolled before their understanding in such orderly sequence,
that although their increase of knowledge was a continuous source
of delight, it never came in shocks of surprise or excited childish
wonderment. I cannot hope to give you more than a faint
conception of the dignity and majesty of a people whose triple
nature was so highly and so harmoniously developed. One principle

governed the three: Truth. They were true to every law under which
they had been created and by which they were sustained. They were
taught from infancy—but of this further on. I wish to reintroduce
Ariadne to you and let her explain some of the wonders of their
teaching, she being herself a teacher.
The observatory was a much used apartment, by both the
family and by guests. It was a library also, and it contained musical
instruments. A balcony encircled it on the outside, and here we often
sat of evenings, especially if the sky was clear and the stars and
moon were shining. The heavens as seen at night were as familiar to
Clytia and Calypso, and even to the children, as a friend’s face.
It was pleasant to sit out upon the balcony even on moonless
nights and when the stars were hidden, and look down upon the city
all brilliantly alight, and listen to the unceasing music of the Falls of
Eudosa. I, too, soon learned his many “moods.”
Back of the house there rose a long succession of hills, ending
finally in snow-capped mountains, the highest of which was called
the Spear, so sharply did it thrust its head up through the clouds into
the heavens.
The lower hills had been converted into vineyards. A couple of
men were fixing the trellises, and Calypso excused himself to his
wife and me and went over to them. A neatly dressed maid came
out of the house and greeted the children, who had much important
news to relate concerning their drive; and a last year’s bird-nest to
show her, which they took pains to explain was quite useless to the
birds, who were all making nice new nests. The sight of the maid,—
evidently an intelligent and well-bred girl,—whose face beamed
affectionately upon the little ones, prompted a question from me:
“How do you manage about your servants, I mean house
servants,” I asked; “do you have people here who are willing to do
menial work?”
Clytia looked up at me with an odd expression. Her answer,
coming from any one less sincere, would have sounded like cant.
“We do not regard any work as mean.”

“But some kinds of work are distasteful, to say the least,” I
insisted.
“Not if you love those for whom you labor,” she returned. “A
mother does not consider any sort of service to her child degrading.”
“O, I know that,” said I; “that is simply natural affection.”
“But natural affection, you know, is only the germ of love. It is
narrow,—only a little broader than selfishness.”
“Well, tell me how it applies in this question of service?” I
asked. “I am not able to comprehend it in the abstract.”
“We do not require people to do anything for us which we
would not do for ourselves, or for them,” she said. “And then, we all
work. We believe in work; it means strength to the body and relief to
the mind. No one permits himself to be served by another for the
unworthy reason, openly or tacitly confessed, that he is either too
proud, or too indolent, to serve himself.”
“Then why have servants at all?” I asked.
“My husband explained to you,” she returned, “that our people
are not all equally rich; and they are not all adapted to what you
would call, perhaps, the higher grades of service. You see the little
maid yonder with the children; she has the gifts of a teacher,—our
teachers are very carefully chosen, and as carefully instructed. She
has been placed with me for our mutual benefit,—I could not intrust
my little ones to the care of a mere paid nurse who thought only of
her wages. Nor could she work simply for wages. The money
consideration is the smallest item in the arrangement. My husband
superintends some steel works in which he has some shares. The
man he is talking with now—who is attending to the grape vines—
has also a large interest in the steel works, but he has no taste or
faculty for engaging in that kind of business. He might spend his
whole life in idleness if he chose, or in mental pursuits, for he is a
very scholarly man, but he loves the kind of work he is doing now,
and our vineyard is his especial pride. Moreover,” a beautiful smile
touched her face as she looked up at the two men on the hillside,
“Fides loves my Calypso, they are soul friends!”

When I became more familiar with the household, I found that
the same relations existed all round; mutual pleasure, mutual
sympathy, mutual helpfulness. First there seemed to be on the part
of each employe a distinct preference and liking for the kind of work
he or she had undertaken to do; second, a fitness and careful
preparation for the work; and last, the love of doing for those who
gave appreciation, love, and another sort of service or assistance in
return. I heard one of them say one day:
“I ask nothing better than to be permitted to cook the meals for
these dear people!”
This was a woman who wrote monthly articles on chemistry and
botany for one of the leading scientific journals. She was a middle-
aged woman and unmarried, who did not wish to live alone, who
abhorred “boarding,” and who had found just such a comfortable
nest in Clytia’s home as suited all her needs and desires. Of course
she did not slave in the kitchen all day long, and her position did not
debar her from the best and most intelligent society, nor cut her off
from the pleasure and privileges that sweeten life. She brought her
scientific knowledge to the preparation of the food she set before us,
and took as much pride in the results of her skill as an inventor
takes in his appliances. And such wholesome, delicious, well-cooked
dishes I have never eaten elsewhere. Clytia believed in intelligently
prepared food, as she believed in intelligent instruction for her
children; she would have thought it a crime to set an ignorant
person over her kitchen. And this woman of whom I am speaking
knew that she held a place of honor and trust, and she filled it not
only with dignity but lovingness. She had some younger women to
assist her, whom she was instructing in the science and the art of
cooking, and who would by-and-by take responsible positions
themselves. These women, or girls, assisted also in the
housekeeping, which was the most perfect system in point of
cleanliness, order and beauty that it is possible to conceive of in a
home; because skill, honesty and conscientiousness enter into every
detail of the life of these people. The body is held in honor, and its
needs are respected. Life is sacred, and physical sins,—neglect or

infringement of the laws of health,—are classed in the same
category with moral transgressions. In fact, the same principles and
the same mathematical rules apply in the Three Natures of Man,—
refined of course to correspond with the ascending scale from the
lowest to the highest, from the physical to the spiritual. But so
closely are the Three allied that there are no dividing lines,—there is
no point where the Mind may say, “Here my responsibility ends,” or
where the Body may affirm, “I have only myself to please.” Day by
day these truths became clear to me. There was nothing particularly
new in anything that I heard,—indeed it was all singularly familiar, in
sound. But the wonder was, that the things we idealize, and theorize
about, they accept literally, and absorb into their lives. They have
made living facts of our profoundest philosophy and our sublimest
poetry. Are we then too philosophical, too poetical,—and not
practical? A good many centuries have rolled up their records and
dropped them into eternity since we were given the simple,
wonderful lesson, “Whatsoever a man sows that shall he also
reap,”—and we have not learned it yet! St. Paul’s voice rings through
the Earth from age to age, “Work out your own salvation,” and we
do not comprehend. These people have never had a Christ—in flesh
and blood—but they have put into effect every precept of our Great
Teacher. They have received the message, from whence I know not,
—or rather by what means I know not,—“A new commandment I
give unto you, that ye love one another.”

Chapter 10.
THE MASTER.
“I spoke as I saw.
I report, as a man may report God’s work—all’s Love, yet all’s
Law.”
— Browning.
I have spoken of Ariadne, and promised to re-introduce her to
you. You will remember her as the graceful girl who accompanied
Clytia and her husband to Thursia. She had not made quite so
strong an impression upon me as had the elder woman, perhaps
because I was so preoccupied with, and interested in watching the
latter’s meeting with Elodia. Certainly there was nothing in the
young woman herself, as I speedily ascertained, to justify
disparagement even with Clytia. I was surprised to find that she was
a member of our charming household.
She was an heiress; but she taught in one of the city schools,
side by side with men and women who earned their living by
teaching. I rather deprecated this fact in conversation with Clytia
one day; I said that it was hardly fair for a rich woman to come in
and usurp a place which rightfully belonged to some one who
needed the work as a means of support,—alas! that I should have
presumed to censure anything in that wonderful country. With
knowledge came modesty.
Clytia’s cheeks crimsoned with indignation. “Our teachers are
not beneficiaries,” she replied; “nor do we regard the positions in our
schools—the teachers’ positions—as charities to be dispensed to the
needy. The profession is the highest and most honorable in our land,
and only those who are fitted by nature and preparation presume to
aspire to the office. There is no bar against those who are so fitted,
—the richest and the most distinguished stand no better, and no

poorer, chance than the poorest and most insignificant. We must
have the best material, wherever it can be found.”
We had but just entered the house, Clytia and I, when Ariadne
glided down the stairs into the room where we sat, and approached
me with the charming frankness and unaffectedness of manner
which so agreeably characterizes the manners of all these people.
She was rather tall, and slight; though her form did not suggest
frailty. She resembled some elegant flower whose nature it is to be
delicate and slender. She seemed even to sway a little, and
undulate, like a lily on its stem.
I regarded her with attention, not unmixed with curiosity,—as a
man is prone to regard a young lady into whose acquaintance he
has not yet made inroads.
My chief impression about her was that she had remarkable
eyes. They were of an indistinguishable, dark color, large horizontally
but not too wide open,—eyes that drew yours continually, without
your being able to tell whether it was to settle the question of color,
or to find out the secret of their fascination, or whether it was simply
that they appealed to your artistic sense—as being something finer
than you had ever seen before. They were heavily fringed at top and
bottom, and so were in shadow except when she raised them toward
the light. Her complexion was pale, her hair light and fluffy; her
brows and lashes were several shades darker than the hair. Her
hands were lovely. Her dress was of course white, or cream, of some
soft, clinging material; and she wore a bunch of blue flowers in her
belt, slightly wilted.
There is this difference in women: some produce an effect
simply, and others make a clear-cut, cameo-like impression upon the
mind. Ariadne was of the latter sort. Whatever she appropriated,
though but a tiny blossom, seemed immediately to proclaim its
ownership and to swear its allegiance to her. From the moment I
first saw her there, the blue flowers in her belt gave her, in my mind,
the supreme title to all of their kind. I could never bear to see
another woman wear the same variety,—and I liked them best when
they were a little wilted! Her belongings suggested herself so vividly

that if one came unexpectedly upon a fan, a book, a garment of
hers, he was affected as by a presence.
I soon understood why it was that my eyes sought her face so
persistently, drawn by a power infinitely greater than the mere
power of beauty; it was due to the law of moral gravitation,—that by
which men are attracted to a leader, through intuitive perception of a
quality in him round which their own energies may nucleate. We all
recognize the need of a centre, of a rallying-point,—save perhaps
the few eccentrics, detached particles who have lost their place in
the general order, makers of chaos and disturbers of peace.
It is this power which constitutes one of the chief qualifications
of a teacher in Lunismar; because it rests upon a fact universally
believed in,—spiritual royalty; an august force which cannot be
ignored, and is never ridiculed—as Galileo was ridiculed, and
punished, for his wisdom; because there ignorance and prejudice do
not exist, and the superstition which planted the martyr’s stake has
never been known.
Ariadne said that she had been up in the observatory, and that
there were indications of an approaching storm.
“I hope it may be a fine one!” exclaimed Clytia.
I thought this rather an extraordinary remark—coming from one
of the sex whose formula is more likely to be, “I hope it will not be a
severe one.”
At that moment a man appeared in the doorway, the majesty of
whose presence I certainly felt before my eyes fell upon him. Or it
might have been the reflection I saw in the countenances of my two
companions,—I stood with my back to the door, facing them,—which
gave me the curious, awe-touched sensation.
I turned round, and Clytia immediately started forward. Ariadne
exclaimed in an undertone, with an accent of peculiar sweetness,—a
commingling of delight, and reverence, and caressing tenderness:
“Ah! the Master!”
Clytia took him by the hand and brought him to me, where I
stood rooted to my place.

“Father, this is our friend,” she said simply, without further
ceremony of introduction. It was enough. He had come on purpose
to see me, and therefore he knew who I was. As for him—one does
not explain a king! The title by which Ariadne had called him did not
at the moment raise an inquiry in my mind. I accepted it as the
natural definition of the man. He was a man of kingly proportions,
with eyes from which Clytia’s had borrowed their limpid blackness.
His glance had a wide compresiveness, and a swift, sure, loving
insight.
He struck me as a man used to moving among multitudes, with
his head above all, but his heart embracing all.
You may think it strange, but I was not abashed. Perfect love
casteth out fear; and there was in this divine countenance—I may
well call it divine!—the lambent light of a love so kindly and so
tender, that fear, pride, vanity, egotism, even false modesty—our pet
hypocrisy—surrendered without a protest.
I think I talked more than any one else, being delicately
prompted to furnish some account of the world to which I belong,
and stimulated by the profound interest with which the Master
attended to every word that I said. But I received an equal amount
of information myself,—usually in response to the questions with
which I rounded up my periods, like this: We do so, and so, upon
the Earth; how is it here? The replies threw an extraordinary light
upon the social order and conditions there.
I naturally dwelt upon the salient characteristics of our people,
—I mean, of course, the American people. I spoke of our enormous
grasp of the commercial principle; of our manipulation of political
and even social forces to great financial ends; of our easy acquisition
of fortunes; of our tremendous push and energy, directed to the
accumulation of wealth. And of our enthusiasms, and institutions;
our religions and their antagonisms, and of the many other things in
which we take pride.
And I learned that in Caskia there is no such thing as
speculative enterprise. All business has an actual basis most
discouraging to the adventurous spirit in search of sudden riches.

There is no monetary skill worthy the dignified appellation of
financial management,—and no use for that particular development
of the talent of ingenuity.
All the systems involving the use of money conduct their affairs
upon the simplest arithmetical rules in their simplest form; addition,
subtraction, multiplication, division. There are banks, of course, for
the mutual convenience of all, but there are no magnificent
delusions called “stocks;” no boards of trade, no bulls and bears, no
“corners,” no mobilizing of capital for any questionable purposes; no
gambling houses; no pitfalls for unwary feet; and no mad fever of
greed and scheming coursing through the veins of men and driving
them to insanity and self-destruction. More than all, there are no
fictitious values put upon fads and fancies of the hour,—nor even
upon works of art. The Caskians are not easily deceived. An
impostor is impossible. Because the people are instructed in the
quality of things intellectual, and moral, and spiritual, as well as in
things physical. They are as sure of the knowableness of art, as they
are—and as we are—of the knowableness of science. Art is but
refined science, and the principles are the same in both, but more
delicately, and also more comprehensively, interpreted in the former
than in the latter.
One thing more: there are no would-be impostors. The law
operates no visible machinery against such crimes, should there be
any. The Master explained it to me in this way:
“The Law is established in each individual conscience, and rests
securely upon self-respect.”
“Great heavens!” I cried, as the wonder of it broke upon my
understanding, “and how many millions of years has it taken your
race to attain to this perfection?”
“It is not perfection,” he replied, “it only approximates
perfection; we are yet in the beginning.”
“Well, by the grace of God, you are on the right way!” said I. “I
am familiar enough with the doctrines you live by, to know that it is
the right way; they are the same that we have been taught,
theoretically, for centuries, but, to tell the truth, I never believed

they could be carried out literally, as you appear to carry them out.
We are tolerably honest, as the word goes, but when honesty
shades off into these hair-splitting theories, why—we leave it to the
preachers, and—women.”
“Then you really have some among you who believe in the
higher truths?” the Master said, and his brows went up a little in
token of relief.—My picture of Earth-life must have seemed a terrible
one to him!
“O, yes, indeed,” said I, taking my cue from this. And I
proceeded to give some character sketches of the grand men and
women of Earth whose lives have been one long, heroic struggle for
truth, and to whom a terrible death has often been the crowning
triumph of their faith. I related to him briefly the history of America
from its discovery four hundred years ago; and told him about the
splendid material prosperity,—the enormous wealth, the
extraordinary inventions, the great population, the unprecedented
free-school system, and the progress in general education and
culture,—of a country which had its birth but yesterday in a deadly
struggle for freedom of conscience; and of our later, crueller war for
freedom that was not for ourselves but for a despised race. I
described the prodigious waves of public and private generosity that
have swept millions of money into burned cities for their rebuilding,
and tons of food into famine-stricken lands for the starving.
I told him of the coming together in fellowship of purpose, of
the great masses, to face a common danger, or to meet a common
necessity; and of the moral and intellectual giants who in outward
appearance and in the seeming of their daily lives are not unlike
their fellows, but to whom all eyes turn for help and strength in the
hour of peril. But I did not at that time undertake any explanation of
our religious creeds, for it somehow seemed to me that these would
not count for much with a people who expressed their theology
solely by putting into practice the things they believed. I had the
thought in mind though, and determined to exploit it later on. As I
have said before, the Master listened with rapt attention, and when I
had finished, he exclaimed,

“I am filled with amazement! a country yet so young, so far
advanced toward Truth!”
He gave himself up to contemplation of the picture I had drawn,
and in the depths of his eyes I seemed to see an inspired prophecy
of my country’s future grandeur.
Presently he rose and went to a window, and, with uplifted face,
murmured in accents of the sublimest reverence that have ever
touched my understanding, “O, God, All-Powerful!”
And a wonderful thing happened: the invocation was responded
to by a voice that came to each of our souls as in a flame of fire,
“Here am I.” The velocity of worlds is not so swift as was our
transition from the human to the divine.
But it was not an unusual thing, this supreme triumph of the
spirit; it is what these people call “divine worship,”—a service which
is never perfunctory, which is not ruled by time or place. One may
worship alone, or two or three, or a multitude, it matters not to God,
who only asks to be worshiped in spirit and in truth,—be the time
Sabbath or mid-week, the place temple, or field, or closet.
A little later I remarked to the Master,—wishing to have a point
cleared up,—
“You say there are no fictitious values put upon works of art;
how do you mean?”
He replied, “Inasmuch as truth is always greater than human
achievement—which at best may only approximate the truth,—the
value of a work of art should be determined by its merit alone, and
not by the artist’s reputation, or any other remote influence,—of
course I do not include particular objects consecrated by association
or by time. But suppose a man paints a great picture, for which he
recieves a great price, and thereafter uses the fame he has won as
speculating capital to enrich himself,—I beg the pardon of every
artist for setting up the hideous hypothesis!—But to complete it: the
moment a man does that, he loses his self-respect, which is about as
bad as anything that can happen to him; it is moral suicide. And he
has done a grievous wrong to art by lowering the high standard he

himself helped to raise. But his crime is no greater than that of the
name-worshipers, who, ignorantly, or insolently, set up false
standards and scorn the real test of values. However, these
important matters are not left entirely to individual consciences;
artists, and so-called art-critics, are not the only judges of art. We
have no mysterious sanctuaries for a privileged few; all may enter,—
all are indeed made to enter, not by violence, but by the simple,
natural means employed in all teaching. All will not hold the brush,
or the pen, or the chisel; but from their earliest infancy our children
are carefully taught to recognize the forms of truth in all art; the eye
was made to see, the ear to hear, the mind to understand.”
The visit was at an end. When he left us it was as though the
sun had passed under a cloud.
Clytia went out with him, her arm lovingly linked in his; and I
turned to Ariadne. “Tell me,” I said, “why is he called Master? Is it a
formal title, or was it bestowed in recognition of the quality of the
man?”
“Both,” she answered. “No man receives the title who has not
the ‘quality.’ But it is in one way perfunctory; it is the distinguishing
title of a teacher of the highest rank.”
“And what are teachers of the highest rank, presidents of
colleges?” I asked.
“O, no,” she replied with a smile, “they are not necessarily
teachers of schools—old and young alike are their pupils. They are
those who have advanced the farthest in all the paths of knowledge,
especially the moral and the spiritual.”
“I understand,” said I; “they are your priests, ministers, pastors,
—your Doctors of Divinity.”
“Perhaps,” she returned, doubtfully; our terminology was not
always clear to those people.
“Usually,” she went on, “they begin with teaching in the schools,
—as a kind of apprenticeship. But, naturally, they rise; there is that
same quality in them which forces great poets and painters to high
positions in their respective fields.”

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