Small World Graphs by the iterated "My Friends are Your Friends'' Principle

Abstract

We study graphs obtained by successive creation and destruction of edges into small neighborhoods of the vertices. Starting with a circle graph of large diameter we obtain small world graphs with logarithmic diameter, high clustering coefficients and a fat tail distribution for the degree. Only local edge formation processes are involved and no preferential attachment was used. Furthermore we found an interesting phase transition with respect to the initial conditions.

Latex, 12 pages with 10 figures

References in corpus (2)

• Growing networks with local rules: preferential attachment, clustering hierarchy and degree correlations
• The "Cameo Principle" and the Origin of Scale-Free Graphs in Social Networks

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