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

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

2003-04-24

arxiv.org/abs/cond-mat/0304563v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

Latex, 12 pages with 10 figures

Scientific paper

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.

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