  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.
