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Smallest small-world network

Takashi Nishikawa·Adilson E. Motter·Ying-Cheng Lai·Frank C. Hoppensteadt
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Abstract

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a single ``center'', from which all shortcuts are connected to uniformly distributed nodes over the network. The networks with several centers and a connected subnetwork of shortcuts are shown to be ``almost'' as efficient. Genetic-algorithm simulations further support our results.

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Takashi Nishikawa, Adilson E. Motter, Ying-Cheng Lai, Frank C. Hoppensteadt. 2002-10-31. Smallest small-world network. https://doi.org/10.1103/physreve.66.046139

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