The Physics of Communicability in Complex Networks

By Ernesto Estrada, Naomichi Hatano, Michele Benzi. arXiv.org, 2011

319 citations recorded by the source corpus.

Abstract A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks.

Subfields: Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dc527fd11456bf0f7015770c0a60fde7da18c2af

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In Statistical and Nonlinear Physics

Citations in the corpus

The ABC Matrix (2016, methodology): “Another interpretation of the Estrada index has been provided in the context of thermal Green’s functions of quantum harmonic oscillators [12,16].”
Random walks and diffusion on networks (2016, background): “ssociated with Q. The matrix on the right-hand side of 18 Eq. (51) is called the \resolvent" of Q. Similar considerations arise in the study of \central" (i.e., important) nodes in networks [142]. The \exit probability" (i.e., the \rst-passage-time probability") is dened as the p”
The structure and dynamics of multilayer networks (2014, background): “Another important measure (when dealing with RWs) is the concept of communicability [216,217], that quantifies the number of possible paths communicating twogivennodes of a network.”