Using network function to define and identify community structure

Abstract

We investigate a functional definition of community structure in complex networks. In particular, we consider networks whose function is enhanced by the ability to synchronize and/or by resilience to node failures. Previous work has shown that the largest eigenvalue of the network's adjacency matrix provides insight into both synchronization and percolation processes. Thus, for networks whose goal is to perform these functions, we propose a method that divides a given network into communities based on maximizing the largest eigenvalues of the adjacency matrices of the resulting communities.