Generating synthetic online social network graph data and topologies
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This document describes a 3-step approach to generating synthetic social network data that respects user privacy: 1. Topology generation uses the R-mat method to create a graph with power law distributions and community structure. Communities are identified using Louvain method. Seed nodes are selected as central nodes in each community. 2. Data attributes like age, gender, interests are defined based on real statistics. Attribute values and their proportions are specified in a table. 3. Data is populated starting from seed nodes using propagation rules. Nearby nodes are more likely to get similar attribute values to their seed. Challenges include disproportionate seed influence and ensuring diversity while meeting proportions.
![Introduction
● Motivation: one of the difficulties for data analysts of
online social networks is the public availability of data,
while respecting the privacy of the users.
● Solution: use synthetically generated data [1].
However, this presents a series of challenges related to
generating a realistic dataset in terms of topologies,
attribute values, communities, data distributions, and so
on.](https://image.slidesharecdn.com/graph-ta-2015-nettletonpresentation-150324035001-conversion-gate01/85/Generating-synthetic-online-social-network-graph-data-and-topologies-2-320.jpg)
![Step 1: Topology generation
We use the R-mat (Recursive MATrix), method [3] to generate an OSN like topology. R-mat
employs a statistical approach and a recursive process to replicate the power law
distributions, skew distributions and community structure (which can be hierarchical),
while maintaining a small diameter for the graph.
The adjacency matrix A of a graph of N nodes is an N N
matrix, with entry a(i, j) = 1 if the edge (i, j) exists, and 0
otherwise.
The adjacency matrix is recursively subdivided into four
equal-sized partitions, and edges are distributed within
these partitions with a unequal probabilities.
Starting from an empty adjacency matrix, edges are
assigned into the matrix one at a time.
For each edge, one of the four partitions is assigned with
probabilities a, b, c, d respectively (a + b + c + d = 1).
The chosen partition is again subdivided into four smaller
partitions, and the procedure is repeated until a simple
cell is obtained (1 1 partition).
The edge is then assigned to this cell of the adjacency
matrix.
Fig. 1. R-mat model
In the current work, we have used the
following probabilities: a=0.45, b=0.15,
c=0.15, d=0.25](https://image.slidesharecdn.com/graph-ta-2015-nettletonpresentation-150324035001-conversion-gate01/85/Generating-synthetic-online-social-network-graph-data-and-topologies-4-320.jpg)
![Step 1: Topology generation
We identify the communities in the
graph structure generated by Rmat, by
processing it with the Louvain[4]
method, which assigns a community
label to each vertex in the graph.
Fig. 2a. Rmat generated topology.
Different colors indicate
communities.](https://image.slidesharecdn.com/graph-ta-2015-nettletonpresentation-150324035001-conversion-gate01/85/Generating-synthetic-online-social-network-graph-data-and-topologies-5-320.jpg)
![Acknowledgements / References
References
[1] D.F. Nettleton, J. Salas, A Data Driven Anonymization Method for Information Rich OSN
Graphs. Submitted to the Journal "Expert Systems with Applications", Dec. 2014.
[2] D.F. Nettleton, Data mining of social networks represented as graphs, Computer Science
Review 7, 1-34 (2013).
[3] D. Chakrabarti, Y. Zhan, C. Faloutsos, R-mat: A recursive model for graph mining, in Proc.
SIAM Data Mining Conference, 2004. SIAM, Philadelphia, PA.
[4] V.D. Blondel, J.L. Guillaume, R. Lambiotte, E. Lefebure, Fast unfolding of communities in
large networks, in Journal of Statistical Mechanics: Theory and Experiment (10), 2008, pp.
1000.
Acknowledgements
This work is partially funded by the Spanish MEC (project TIN2013-49814-EXP).](https://image.slidesharecdn.com/graph-ta-2015-nettletonpresentation-150324035001-conversion-gate01/85/Generating-synthetic-online-social-network-graph-data-and-topologies-12-320.jpg)
Generating synthetic online social network graph data and topologies
- 1. 3rd Workshop on Graph-based Technologies and Applications (Graph-TA) UPC, Barcelona
- 2. Introduction ● Motivation: one of the difficulties for data analysts of online social networks is the public availability of data, while respecting the privacy of the users. ● Solution: use synthetically generated data [1]. However, this presents a series of challenges related to generating a realistic dataset in terms of topologies, attribute values, communities, data distributions, and so on.
- 3. Introduction In the following we present an approach for generating a graph topology and populating it with synthetic data to simulate an online social network. 3 Steps Data Definition Topology Generation Data Population
- 4. Step 1: Topology generation We use the R-mat (Recursive MATrix), method [3] to generate an OSN like topology. R-mat employs a statistical approach and a recursive process to replicate the power law distributions, skew distributions and community structure (which can be hierarchical), while maintaining a small diameter for the graph. The adjacency matrix A of a graph of N nodes is an N N matrix, with entry a(i, j) = 1 if the edge (i, j) exists, and 0 otherwise. The adjacency matrix is recursively subdivided into four equal-sized partitions, and edges are distributed within these partitions with a unequal probabilities. Starting from an empty adjacency matrix, edges are assigned into the matrix one at a time. For each edge, one of the four partitions is assigned with probabilities a, b, c, d respectively (a + b + c + d = 1). The chosen partition is again subdivided into four smaller partitions, and the procedure is repeated until a simple cell is obtained (1 1 partition). The edge is then assigned to this cell of the adjacency matrix. Fig. 1. R-mat model In the current work, we have used the following probabilities: a=0.45, b=0.15, c=0.15, d=0.25
- 5. Step 1: Topology generation We identify the communities in the graph structure generated by Rmat, by processing it with the Louvain[4] method, which assigns a community label to each vertex in the graph. Fig. 2a. Rmat generated topology. Different colors indicate communities.
- 6. Step 1: Topology generation Next we identify a set of seed vertices which will be used as the starting points for propagating the data. • For each community, we find the medoid node in terms of the statistical and topological qualities (especially centrality and degree). • We can progressively assign seed vertices which give an optimal coverage of the complete graph, while not overlapping in their immediate neighborhoods (to avoid overwriting data propagated from different seeds). Fig. 2b. Rmat generated topology with seed nodes indicated.
- 7. Step 2: Data definition • The choice of data will be application specific. • The distributions of the values of the different attributes should be similar to those of some real social network (ground truth). • In order to achieve this, we can use sources of official statistics, such as government census data www.indexmundi.com, www.census.gov, www.bls.gov • Statistical summaries made public by the social network providers, such as Facebook: www.adweek.com, fanpagelist.com, http://royal.pingdom.com/2009/11/27/study-males- vs-females-in-social-networks/ • We may also need some lookup tables for inter-related attribute values. For example, for the age group “18-25”, there will be a much higher proportion of “profession=student” and “marital status=single”, and for “gender=male” there will be a higher proportion of “like3=soccer club”. • Another option for ‘ground truth’ are publicly available OSN datasets, such as: SNAP: http://snap.stanford.edu/data/#communities
- 8. Step 2: Data definition Attribute Values Age "18-25", (32%) "26-35", (26%) "36-45" (20%) ,"46-55" (13%) ,"56-65" (9%) Gender male (47%), female (53%) Residence "Palo Alto“ (17%), "Santa Barbara“ (16%), "Boca Raton“ (16%), "Boston“ (17%), "Norfolk“ (17%), "San Jose“ (17%) Religion "Christian" (31.9%), "Hindu" (14.8%), "Jewish" (0.2%), "Muslim" (27.1%), "Sikh" (0.3%), "Traditional Spirituality" (0.1%), "Other Religions" (12.9%), "No religious affiliation" (12.7%) Marital status "Single" (31.5%), "Married" (51.4%), "Divorced" (10.5%), "Widowed" (6.6%) Profession (ISCO-08 structure) "Manager" (12.2%), "Professional" (17.1%), "Service" (13.9%), "Sales and office" (17.8%), “Student” (23%), "Natural resources construction and maintenance" (7.0%), "Production transportation and material moving" (9.0%) Political orientation "Far Left" (9.4%), "Left" (34.7%),"Center Left", (18.1%), "Center" (18.0%), "Center Right" (10.5%), "Right" (8.0%), "Far Right" (1.3%) {like1, like2, like3} Patterns: {"entertainment", "entertainment", "music artist"} (25%), {"music artist", "music artist", "entertainment"} (25%), {"drink brand", "drink brand", "entertainment"} (25%), {"tv show", "drink brand", "soccer club"} (25%). Table 1. Example attributes, attribute-values and their proportions.
- 9. Step 3: Data population In order to optimize the assignment, we can use a fitness function and find the optimum configuration using a stochastic process. Fitness = (, , ) where = set of seed assignments, = set of data propagation rules and thresholds, = set of required data distributions. We initiate the data population of the network using the set of seed nodes. The rest of the nodes will be assigned data by a propagation from the seed nodes. The immediate neighbors of a seed will have a higher probability of being assigned similar attribute values. For each hop further from the seed node, the influence of the seed node on other nodes is progressively reduced. However, we give precedence to seed nodes in the same community as the node to be assigned. We can also use ontologies /taxonomies and a distance measure to assign similar, rather than identical values (with an appropriate threshold) when propagating attribute-values. The influence on assignment by the seed node has to be traded off by the desired overall proportions of the attribute values (diversity).
- 10. Step 3: Data population Fig. 3. Data propagation from seed nodes and topology of Fig. 1.
- 11. Challenges A high degree node chosen as a seed may have a disproportionate influence on the network. The synthetic data generation may create fictitious user profiles (combinations of attribute-values). The restrictions on the placement of the seed nodes and the topology of the communities may cause a significant percentage of nodes to have random assignments (coverage). Making the communities representative of key attribute-value profiles Obtaining ‘ground truth’.
- 12. Acknowledgements / References References [1] D.F. Nettleton, J. Salas, A Data Driven Anonymization Method for Information Rich OSN Graphs. Submitted to the Journal "Expert Systems with Applications", Dec. 2014. [2] D.F. Nettleton, Data mining of social networks represented as graphs, Computer Science Review 7, 1-34 (2013). [3] D. Chakrabarti, Y. Zhan, C. Faloutsos, R-mat: A recursive model for graph mining, in Proc. SIAM Data Mining Conference, 2004. SIAM, Philadelphia, PA. [4] V.D. Blondel, J.L. Guillaume, R. Lambiotte, E. Lefebure, Fast unfolding of communities in large networks, in Journal of Statistical Mechanics: Theory and Experiment (10), 2008, pp. 1000. Acknowledgements This work is partially funded by the Spanish MEC (project TIN2013-49814-EXP).
- 13. Thank you for your attention !