Introduction to Complex Networks
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This document introduces complex networks and the R programming language. It defines what networks are, provides examples of complex networks, and discusses key metrics used to characterize complex networks such as degree distribution, diameter, and clustering coefficient. It then introduces R as a programming language for statistical computing and graphics. The document discusses installing R packages and features of R including being open source and operating system independent. It also introduces the iGraph package for manipulating graphs in R and provides examples of creating and analyzing a random graph.
![Some basic definitions: Degree distribution
▶ Degree d(i) of vertex i: number of edges
incident on i
▶ Degree Sequence:
[d(1), d(2), d(3), d(4), d(5)] = [2, 2, 3, 2, 1]
▶ Degree Distribution: [(1, 1); (2, 3); (3, 1)]
1
2
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Saeed Rahmani (ZNU) R and iGraph October 30, 2016 5 / 21](https://image.slidesharecdn.com/introductiontocomplexnetworks-170709215255/85/Introduction-to-Complex-Networks-5-320.jpg)
Introduction to Complex Networks
- 1. Introduction to Complex Networks Saeed Rahmani University of Zanjan rahmanidashti@gmail.com October 30, 2016 Saeed Rahmani (ZNU) R and iGraph October 30, 2016 1 / 21
- 2. . What is a network? .. ...... Network is a collection of entities that are interconnected with links. - Flavia Bonomo Saeed Rahmani (ZNU) R and iGraph October 30, 2016 2 / 21
- 3. Examples ▶ People that are friends ▶ Computers that are interconnected ▶ Web pages that point to each other ▶ Proteins that interact In terms of graph theory, the entities are called vertices and the links edges. Saeed Rahmani (ZNU) R and iGraph October 30, 2016 3 / 21
- 4. What is a Complex Network? Large graphs of real life are called complex networks. Some of the main questions about them are the following: ▶ What are the statistics of real life networks? ▶ Can we explain how the networks were generated? Saeed Rahmani (ZNU) R and iGraph October 30, 2016 4 / 21
- 5. Some basic definitions: Degree distribution ▶ Degree d(i) of vertex i: number of edges incident on i ▶ Degree Sequence: [d(1), d(2), d(3), d(4), d(5)] = [2, 2, 3, 2, 1] ▶ Degree Distribution: [(1, 1); (2, 3); (3, 1)] 1 2 3 45 Saeed Rahmani (ZNU) R and iGraph October 30, 2016 5 / 21
- 6. Some basic definitions: Diameter ▶ Diameter: the length of the longest shortest path between two vertices of the graph 1 2 3 45 Saeed Rahmani (ZNU) R and iGraph October 30, 2016 6 / 21
- 7. Some basic definitions: Clustering coefficient ▶ Clustering coefficient of vertex i : • if d(i) > 1, is the number of edges between neighbors of i divided by d(i)(d(i) − 1)/2 • if d(i) <= 1 can be defined as 0 or 1 ▶ clustering coefficient of vertex 3 : 1/6 ▶ clustering coefficient of vertex 1 : 1 1 2 3 4 5 Saeed Rahmani (ZNU) R and iGraph October 30, 2016 7 / 21
- 8. Characterization of complex networks ▶ Diameter, Clustering coefficient, Degree distribution. ▶ Betweenness centrality: number of short paths going through a vertex. ▶ Communities: can one identify cliques within the network? ▶ Local motifs: What is the structure of the building blocks of complex networks? Motifs: Subgraphs that have a signifficantly higher density in the ob- served network than in the randomizations of the same (ID, Adj-Matrix). ▶ Hubs: Nodes with higher degree (greater than 5, 8, 12, or 20) Saeed Rahmani (ZNU) R and iGraph October 30, 2016 8 / 21
- 9. . R Programming .. ...... R is a programming language and software environment for statis- tical computing and graphics. Saeed Rahmani (ZNU) R and iGraph October 30, 2016 9 / 21
- 10. . R Package .. ...... It compiles and runs on a wide variety of UNIX platforms, Win- dows and Mac OS. R can be downloaded and installed from CRAN website , CRAN stands for Comprehensive R Archive Network and Bioconductor. - https://cran.r-project.org/ - https://www.bioconductor.org/ Saeed Rahmani (ZNU) R and iGraph October 30, 2016 10 / 21
- 11. Install Package Saeed Rahmani (ZNU) R and iGraph October 30, 2016 11 / 21
- 12. Features ▶ Open Source The source code of R program and the extensions could be examined line by line. ▶ Integrating with other Programming Language R is an interpreting language, can be rather slow, but could integrate with high ecient languages such as C, C++ or Fortran. ▶ OS Independence: UNIX, Linux, Windows, MacOS, FreeBSD. ▶ Command line Driven You have to write Commands. Saeed Rahmani (ZNU) R and iGraph October 30, 2016 12 / 21
- 13. IDE ▶ R GUI Saeed Rahmani (ZNU) R and iGraph October 30, 2016 13 / 21
- 14. IDE - Con ▶ R Studio (- http://www.rstudio.com) Saeed Rahmani (ZNU) R and iGraph October 30, 2016 14 / 21
- 15. Web App Development ▶ Shiny (- http://www.rstudio.com/shiny) Shiny makes it super simple for R users like you to turn analyses into interactive web applications that anyone can use Saeed Rahmani (ZNU) R and iGraph October 30, 2016 15 / 21
- 16. iGraph Saeed Rahmani (ZNU) R and iGraph October 30, 2016 16 / 21
- 17. Creating and Using Graphs ▶ Manipulating graphs with R is typically done with the igraph pack- age, so lets try it out: First Off, install igraph and attach it with the usual code . install igraph .. ...... install.packages(”igraph”) library(igraph) Saeed Rahmani (ZNU) R and iGraph October 30, 2016 17 / 21
- 18. Create a Random Graph ▶ For exploration sake, lets generate a random graph (An Erdos-Renyi random graph) . random graph .. ...... randomGraph = erdos.renyi.game(20, 0.2) plot(randomGraph) Saeed Rahmani (ZNU) R and iGraph October 30, 2016 18 / 21
- 19. Summary Statistics . degree .. ......hist(degree(randomGraph)) Saeed Rahmani (ZNU) R and iGraph October 30, 2016 19 / 21
- 20. Acknowledgments: To Flavia Bonomo, for his Slide. Saeed Rahmani (ZNU) R and iGraph October 30, 2016 20 / 21
- 21. Questions? Saeed Rahmani (ZNU) R and iGraph October 30, 2016 21 / 21