Kinetic Theory of Random Graphs: from Paths to Cycles

Details Kinetic Theory of Random Graphs: from Paths to Cycles Kinetic Theory of Random Graphs: from Paths to Cycles

2004-08-27

arxiv.org/abs/cond-mat/0408620v1

Phys. Rev. E 71 026129 (2005)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 10 figures

Scientific paper

10.1103/PhysRevE.71.026129

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.

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