Small worlds: how and why.
We investigate small-world networks from the point of view of their origin. While the characteristics of small-world networks are now fairly well understood, there is as yet no work on what drives the emergence of such a network architecture. In situations such as neural or transportation networks, where a physical distance between the nodes of the network exists, we study whether the small-world topology arises as a consequence of a tradeoff between maximal connectivity and minimal wiring. Using simulated annealing, we study the properties of a randomly rewired network as the relative tradeoff between wiring and connectivity is varied. When the network seeks to minimize wiring, a regular graph results. At the other extreme, when connectivity is maximized, a "random" network is obtained. In the intermediate regime, a small-world network is formed. However, unlike the model of Watts and Strogatz [Nature 393, 440 (1998)], we find an alternate route to small-world behavior through the formation of hubs, small clusters where one vertex is connected to a large number of neighbors.
Mathias
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N
Department of Computer Science and Automation, Indian Institute of Science, Bangalore 560 012, India. nisha@csa.iisc.ernet.in
Gopal
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D000465:Algorithms; D000818:Animals; D055592:Biophysical Phenomena; D001703:Biophysics; D001921:Brain / Q000473:pathology; D006801:Humans; D008954:Models, Biological; D008959:Models, Neurological; D008962:Models, Theoretical; D016571:Neural Networks, Computer