Detecting Community Structures in Networks Using a Linear-Programming Based Approach: a Review

Abstract

We give an account of an approach to community-structure detection in networks using linear programming: given a finite simple graph G, we assign penalties for manipulating this graph by either deleting or adding edges, and then consider the problem of turning G, by performing these two operations, at minimal total cost into a graph that represents a community structure, i.e., that is a disjoint union of complete subgraphs. We show that this minimization problem can be reformulated (and solved!) in terms of a one-parameter family of linear-programming problems relative to which some kind of a “second-order phase transition” can be observed, and we demonstrate by example that this interpretation provides a viable alternative for dealing with the much studied task of detecting community structures in networks. And by reporting our discussions with a leading ecologist, we demonstrate how our approach can be used to analyse food webs and to support the elucidation of their “global” implications.