Entropy measures for complex networks: toward an information theory of complex topologies
Originally posted at http://arxiv.org/abs/0907.1514v2. Preprint of an article published in Physical Review E, 2009.
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.
Kartik Anand and Ginestra Bianconi. "Entropy measures for complex networks: toward an information theory of complex topologies" Physics Faculty Publications (2009).
Available at: http://works.bepress.com/gbianconi/4