Maximal entropy random networks with given degree distribution
M. Bauer, D. Bernard
TL;DR
This paper introduces a maximum entropy-based model for random graphs with specified degree distributions, analyzing their structural properties and percolation behavior within a statistical mechanics framework.
Contribution
It develops a novel maximum entropy approach to model random graphs with arbitrary degree distributions, including analysis of percolation and component structure.
Findings
Derived free energy and component distribution formulas
Identified percolation threshold and cluster size
Extended analysis to oriented graphs
Abstract
Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the distribution of connected components. We determine the size of the percolation cluster above the percolation threshold. The conditional degree distribution on the percolation cluster is also given. We briefly present the analogous discussion for oriented graphs, giving for example the percolation criterion.
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Taxonomy
TopicsComplex Network Analysis Techniques · Opinion Dynamics and Social Influence · Theoretical and Computational Physics