On the properties of small-world network models Export

@article{citeulike:274569, 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]}, author = {Barrat, A. and Weigt, M.}, citeulike-article-id = {274569}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s100510050067}, citeulike-linkout-1 = {http://www.metapress.com/content/0HGUCD51T90CKB12}, citeulike-linkout-2 = {http://www.springerlink.com/content/0hgucd51t90ckb12}, day = {19}, doi = {10.1007/s100510050067}, journal = {The European Physical Journal B - Condensed Matter and Complex Systems}, keywords = {complex-networks}, month = {January}, number = {3}, pages = {547--560}, posted-at = {2009-01-05 09:45:11}, priority = {3}, title = {On the properties of small-world network models}, url = {http://dx.doi.org/10.1007/s100510050067}, volume = {13}, year = {2000} }

TY - JOUR ID - citeulike:274569 L3 - citeulike-article-id:274569 N2 - 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] IS - 3 JF - The European Physical Journal B - Condensed Matter and Complex Systems EP - 560 TI - On the properties of small-world network models VL - 13 SP - 547 KW - complex-networks AU - Barrat, A AU - Weigt, M PY - 2000/01/19/ UR - http://dx.doi.org/10.1007/s100510050067 ER -