Temperature in complex networks

Details Temperature in complex networks Temperature in complex networks

2006-06-30

arxiv.org/abs/cond-mat/0606805v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 table

Scientific paper

Various statistical-mechanics approaches to complex networks have been proposed to describe expected topological properties in terms of ensemble averages. Here we extend this formalism by introducing the fundamental concept of graph temperature, controlling the degree of topological optimization of a network. We recover the temperature-dependent version of various important models as particular cases of our approach, and show examples where, remarkably, the onset of a percolation transition, a scale-free degree distribution, correlations and clustering can be understood as natural properties of an optimized (low-temperature) topology. We then apply our formalism to real weighted networks and we compute their temperature, finding that various techniques used to extract information from complex networks are again particular cases of our approach.

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