Higher-order distributions and nongrowing complex networks without multiple connections

Tomas Hruz, Michal Natora, and Madhuresh Agrawal
Phys. Rev. E 77, 046101 – Published 2 April 2008

Abstract

We study stochastic processes that generate nongrowing complex networks without self-loops and multiple edges (simple graphs). The work concentrates on understanding and formulation of constraints which keep the rewiring stochastic processes within the class of simple graphs. To formulate these constraints a different concept of wedge distribution (paths of length 2) is introduced and its relation to degree-degree correlation is studied. The analysis shows that the constraints, together with edge selection rules, do not even allow the formulation of a closed master equation in the general case. We also introduce a particular stochastic process which does not contain edge selection rules, but which, we believe, can provide some insight into the complexities of simple graphs.

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  • Received 20 August 2007

DOI:https://doi.org/10.1103/PhysRevE.77.046101

©2008 American Physical Society

Authors & Affiliations

Tomas Hruz

  • Institute of Theoretical Computer Science, ETH Zürich, Universitätstrasse 6, 8092 Zürich, Switzerland

Michal Natora

  • Department of Software Engineering and Theoretical Computer Science, Berlin Institute of Technology, Strasse des 17 Juni 135, 10623 Berlin, Germany

Madhuresh Agrawal

  • Department of Computer Science and Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, Utter Pradesh, India

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Issue

Vol. 77, Iss. 4 — April 2008

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