Epsilon Equitable Partitions based Approach for Role & Positional Analysis of Social Networks

Abstract

In social network analysis, the fundamental idea behind the notion of position is to discover actors who have similar structural signatures. Positional analysis of social networks involves partitioning the actors into disjoint sets using a notion of equivalence which captures the structure of relationships among actors. Classical approaches to Positional Analysis, such as Regular equivalence and Equitable Partitions, are too strict in grouping actors and often lead to trivial partitioning of actors in real world networks. An $\epsilon$-Equitable Partition ($\epsilon$EP) of a graph is an useful relaxation to the notion of structural equivalence which results in meaningful partitioning of actors. All these methods assume a single role per actor, actors in real world tend to perform multiple roles. For example, a Professor can possibly be in a role of "Advisor" to his PhD students, but in a role of "Colleague" to other Professors in his department. In this thesis we propose epsilon-equitable partitions based approaches to perform scalable positional analysis and to discover positions performing multiple roles. First, we propose and implement a new scalable distributed algorithm based on MapReduce methodology to find $\epsilon$EP of a graph. Empirical studies on random power-law graphs show that our algorithm is highly scalable for sparse graphs, thereby giving us the ability to study positional analysis on very large scale networks. Second, we propose a new notion of equivalence for performing positional analysis of networks using multiple epsilon-equitable partitions. These multiple partitions give us a better bound on identifying equivalent actor "positions" performing multiple "roles". Evaluation of our methods on multi-role ground-truth networks and time evolving snapshots of real world social graphs show the importance of epsilon equitable partitions for discovering positions performing multiple roles and in studying the evolution of actors and their ties.

Publication
MS by Research Thesis, Department of Computer Science and Engineering, Indian Institute of Technology (IIT) Madras. May 2015.
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