THE SMALL-WORLD PROPERTY IN NETWORKS GROWING BY ACTIVE EDGES

Philippe J. Giabbanelli ()
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Philippe J. Giabbanelli: MoCSSy Program, The IRMACS Centre, Simon Fraser University, 8888 University Drive, Burnaby V5A 1S6, Canada

Advances in Complex Systems (ACS), 2011, vol. 14, issue 06, 853-869

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.

Keywords: Structures and organization in complex systems; patterns; fractals (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0219525911003207

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