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.
%0 Journal Article
%1 anand_entropy_2009
%A Anand, Kartik
%A Bianconi, Ginestra
%D 2009
%J Physical Review E
%K analysis, entropy, network physics statistical
%N 4
%P 045102
%R 10.1103/PhysRevE.80.045102
%T Entropy measures for networks: Toward an information theory of complex topologies
%U http://pre.aps.org/abstract/PRE/v80/i4/e045102
%V 80
%X 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.
@article{anand_entropy_2009,
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.},
added-at = {2017-01-09T13:57:26.000+0100},
author = {Anand, Kartik and Bianconi, Ginestra},
biburl = {https://www.bibsonomy.org/bibtex/222cdf6a2035c9c8165f4c41daffefeea/yourwelcome},
doi = {10.1103/PhysRevE.80.045102},
interhash = {75afb81b46225b1b01ba5724333e008b},
intrahash = {22cdf6a2035c9c8165f4c41daffefeea},
journal = {Physical Review E},
keywords = {analysis, entropy, network physics statistical},
number = 4,
pages = 045102,
shorttitle = {Entropy measures for networks},
timestamp = {2017-01-09T14:01:11.000+0100},
title = {Entropy measures for networks: {Toward} an information theory of complex topologies},
url = {http://pre.aps.org/abstract/PRE/v80/i4/e045102},
urldate = {2013-09-24},
volume = 80,
year = 2009
}