The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.
On the properties of small-world network models
Abstract
Abstract:We study the small-world networks recently introduced by Watts and Strogatz [Nature 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. [0.5cm]
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Cites
Scaling Concepts in Polymer Physics
de Gennes, P. G., & Witten, T. A. (1980) · Physics Today · doi:10.1063/1.2914118 · Cited by 9,348
Bollobás, B. (1985) · Cited by 6,196
Renormalization group analysis of the small-world network model
Newman, M. E. J., & Watts, D. J. (1999) · Physics Letters A · doi:10.1016/s0375-9601(99)00757-4 · Cited by 1,448
Scaling and percolation in the small-world network model
Newman, M. E. J., & Watts, D. J. (1999) · Physical Review E · doi:10.1103/physreve.60.7332 · Cited by 1,202
Monte Carlo Simulation in Statistical Physics: An Introduction
Binder, K., & Heermann, D. W. (2019) · Graduate Texts in Physics · doi:10.1007/978-3-030-10758-1 · Cited by 879
Comment on ``Small-world networks: Evidence for a crossover picture''Preprint
Barrat, A. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.cond-mat/9903323 · Cited by 13
Self-citation
Cited by
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Efficient behavior of small-world networks
Latora, V., & Marchiori, M. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.198701 · Cited by 5,119
Dorogovtsev, S. N., & Mendes, J. F. F. (2002) · Advances in Physics · doi:10.1080/00018730110112519 · Cited by 3,171
Metadata
- Authors
- Barrat, A., & Weigt, M.
- Venue
- The European Physical Journal B
- Published
- 2000-01
- Volume
- 13
- Issue
- 3
- Pages
- 547-560
- ISSN
- 1434-6028 (ISSN-L)
- OpenAlex
- W1991306266
- Cited by
- 888
- References
- 6
- FWCI
- 21.38
- Type
- journal article
- Language
- en
- Open access
- closed
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