Small worlds: how and why.

N Mathias; V Gopal

doi:10.1103/physreve.63.021117

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Small worlds: how and why.

N Mathias·V Gopal

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Abstract

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.

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Algorithms Animals Biophysical Phenomena Biophysics Brain Humans Models, Biological Models, Neurological Models, Theoretical Neural Networks, Computer Journal Article Research Support, Non-U.S. Gov't

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N Mathias, V Gopal. 2001-01-26. Small worlds: how and why.. https://doi.org/10.1103/physreve.63.021117

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