Communicability and Bipartivity in Complex Networks at Negative Temperatures

Introduction Bipartivity is an important property that arises naturally in many contexts of network study (Estrada and Rodriguez-Velazquez, 2005). Strictly, an undirected, unweighted network is said to be bipartite if the nodes can be divided into two disjoint subsets such that all edges link from one subset to the other. More generally, it is of interest to know whether a network contains subnetworks that are approximately bipartite. In the context of protein-protein interactions, the bipartite structure is intimately connected with the existence of complementary binding domains (Thomas et al., 2003; Morrison et al. 2006). In this work our aim is to introduce a natural, computable, and physically appealing way to discover bipartite subgraphs in complex networks. Our approach fits into the realm of spectral graph theory—the basic measure can be neatly described in terms of eigenvectors and eigenvalues of the adjacency matrix. Results We start by considering the communicability between a pair of nodes p and q in the