Scalable Positional Analysis for Studying Evolution of Nodes in Networks

TL;DR

This paper introduces a scalable distributed algorithm for positional analysis in large social networks, enabling meaningful actor grouping and studying network evolution efficiently.

Contribution

It presents a novel MapReduce-based algorithm for Epsilon Equitable Partitions, improving scalability for analyzing large, dynamic social networks.

Findings

Algorithm is highly scalable for sparse graphs

Effective on large-scale Facebook and Flickr data

Reveals insights into network evolution

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 (EEP) of a graph, which is similar in spirit to Stochastic Blockmodels, is a useful relaxation to the notion of structural equivalence which results in meaningful partitioning of actors. In this paper we propose and implement a new scalable distributed algorithm based on MapReduce methodology to find EEP 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. We also present the results of our algorithm on time evolving snapshots of the facebook and flickr social graphs. Results show the importance of positional analysis on large dynamic networks.