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The Small-World Property In Networks Growing By Active Edges

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  • PHILIPPE J. GIABBANELLI

    (MoCSSy Program, The IRMACS Centre, Simon Fraser University, 8888 University Drive, Burnaby V5A 1S6, Canada)

Abstract

In the last three years, we have witnessed an increasing number of complex network models based on a 'fractal' approach, in which parts of the network are repeatedly replaced by a given pattern. Our focus is on models that can be defined by repeatedly adding a pattern network to selected edges, calledactiveedges. We prove that when a pattern network has at least two active edges, then the resulting network has an average distance at most logarithmic in the number of nodes. This suggests that real-world networks based on a similar growth mechanism are likely to have small average distance. We provide an estimate of the clustering coefficient and verify its accuracy using simulations. Using numerous examples of simple patterns, our simulations show various ways to generate small-world networks. Finally, we discuss extensions to our framework encompassing probabilistic patterns and active subnetworks.

Suggested Citation

  • Philippe J. Giabbanelli, 2011. "The Small-World Property In Networks Growing By Active Edges," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 853-869.
    • Handle: RePEc:wsi:acsxxx:v:14:y:2011:i:06:n:s0219525911003207
    DOI: 10.1142/S0219525911003207
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