Alternate Title

Entropy measures for networks: toward an information theory of complex topologies

Abstract

The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.

Notes

Originally posted at http://arxiv.org/abs/0907.1514v2. Preprint of an article published in Physical Review E, 2009.

Keywords

disordered systems, neural networks, entropy measures, complex networks, Gibbs and von Neumann entropies, Shannon entropy

Subject Categories

Condensed matter, Topology

Disciplines

Physics

Publication Date

2009

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