On the properties of small-world network models

Details On the properties of small-world network models On the properties of small-world network models

1999-03-29

arxiv.org/abs/cond-mat/9903411v2

Europ. Phys. J. B 13, 547 (2000)

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages including 15 figures, version accepted for publication in EPJ B

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the properties of small-world network models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the properties of small-world network models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the properties of small-world network models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-227606