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Journal Articles The European Physical Journal B Year : 2000

On the properties of small-world network models

A. Barrat


We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a ``small-world'' behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a ``small-world'' one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite.

Dates and versions

insu-03726416 , version 1 (18-07-2022)



A. Barrat, M. Weigt. On the properties of small-world network models. The European Physical Journal B, 2000, 13, pp.547-560. ⟨insu-03726416⟩


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