Statistical Mechanics of Multi-Edge Networks

Abstract

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos variables and those where they account for discrete, distinguishable events, which we call multi-edge networks. In this work we face this problem introducing multi-edge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multi-edges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multi-edge processes. The implications of these results are important as many real agent based problems mapped onto graphs require of this treatment for a proper characterization of its collective behavior.

17 pages (13 + Appendix), 3 figures, Submitted to PRX

References in corpus (7)

• Spectral properties of the Laplacian of multiplex networks
• The entropy of randomized network ensembles
• Maximum likelihood: extracting unbiased information from complex networks
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Correlations in weighted networks
• Entropies of complex networks with hierarchically constrained topologies
• An ensemble approach to the analysis of weighted networks

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• Classical Information Theory of Networks
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