Kinetic Theory of Random Graphs: from Paths to Cycles

2004/08/27 by E. Ben-Naim, P. L. Krapivsky · 1 citation
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.71.026129

published as Phys. Rev. E 71 026129 (2005) · 11 pages, 10 figures

arxiv created 2004/08/27 · arxiv updated 2009/12/01

Abstract

Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically. At the gelation point, the typical length of paths and cycles, l, scales with the component size k as l ~ k^1/2. Dynamic and finite-size scaling laws for the behavior at and near the gelation point are obtained. Finite-size scaling laws are verified using numerical simulations.

Cited by

• Nonreciprocal random networks and their percolation properties

Related

• Kinetic Theory of Random Graphs
• Unicyclic components in random graphs
• Scale-free property for degrees and weights in an N-interactions random graph model
• Growing random networks under constraints
• A self-organized graph evolution model with preferential network random walk