Small world graphs by iterated local edge formation

Ph Blanchard; T. Krueger; A. Ruschhaupt

doi:10.1103/PhysRevE.71.046139

Small world graphs by iterated local edge formation

Ph Blanchard
, T. Krueger
, A. Ruschhaupt

Bielefeld University
University of the Basque Country

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	046139
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	71
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevE.71.046139
Publication status	Published - Apr 2005
Externally published	Yes

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10.1103/PhysRevE.71.046139

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title = "Small world graphs by iterated local edge formation",

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.",

author = "Ph Blanchard and T. Krueger and A. Ruschhaupt",

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AB - 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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DO - 10.1103/PhysRevE.71.046139

M3 - Article

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SN - 1539-3755

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JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 4

M1 - 046139

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Small world graphs by iterated local edge formation

Abstract

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