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 Rapid Communication 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.
authors.affiliation: The Abdus Salam International Center for Theoretical Physics, Trieste, Italy.
authors.forename: Kartik
authors.initials: K
authors.lastname: Anand
authors.forename: Ginestra
authors.initials: G
authors.lastname: Bianconi
mesh_terms: D003198:Computer Simulation; D019277:Entropy; D008954:Models, Biological; D009415:Nerve Net / Q000502:physiology*; D015398:Signal Transduction / Q000502:physiology*; D012944:Social Support