Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 40, Issue 32, Pages 9723-9732Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/40/32/001
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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.
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