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Construction of equilibrium networks with an energy function
We construct equilibrium networks by introducing an energy function depending
on the degree of each node as well as the product of neighboring degrees. With
this topological energy function, networks constitute a canonical ensemble,
which follows the Boltzmann distribution for given temperature. It is observed
that the system undergoes a topological phase transition from a random network
to a star or a fully-connected network as the temperature is lowered. Both
mean-field analysis and numerical simulations reveal strong first-order phase
transitions at temperatures which decrease logarithmically with the system
size. Quantitative discrepancies of the simulation results from the mean-field
prediction are discussed in view of the strong first-order nature.Comment: To appear in J. Phys.