Statistical mechanics of random graphs

Equilibrium statistical mechanics on correlated random graphs

Biological and social networks have recently attracted enormous attention between physicists. Among several, two main aspects may be stressed: A non trivial topology of the graph describing the mutual interactions between agents exists and/or, typically, such interactions are essentially (weighted) imitative. Despite such aspects are widely accepted and empirically confirmed, the schemes curren...

2 00 3 Statistical mechanics of random graphs

We discuss various aspects of the statistical formulation of the theory of random graphs, with emphasis on results obtained in a series of our recent publications. PACS numbers: 02.50.Cw, 05.40.-a, 05.50.+q, 87.18.Sn The backbone of a generic complex system can be represented by a graph: the nodes refer to the system subunits and the links represent the interactions. Such a representation can b...

On random graphs and the statistical mechanics of granular matter

– The dynamics of spins on a random graph with ferromagnetic three-spin interactions is used to model the compaction of granular matter under a series of taps. Taps are modelled as the random flipping of a small fraction of the spins followed by a quench at zero temperature. We find that the density approached during a logarithmically slow compaction the random-close-packing density corresponds...

Statistical Mechanics and Algorithms on Sparse and Random Graphs

Statistical mechanics on isoradial graphs

Isoradial graphs are a natural generalization of regular graphs which give, for many models of statistical mechanics, the right framework for studying models at criticality. In this survey paper, we first explain how isoradial graphs naturally arise in two approaches used by physicists: transfer matrices and conformal field theory. This leads us to the fact that isoradial graphs provide a natur...