Kinetic Theory of Random Graphs
E. Ben-Naim, P.L. Krapivsky
TL;DR
This paper applies kinetic theory to analyze the statistical properties of evolving random graphs, deriving analytical expressions for structural features and scaling laws for finite systems.
Contribution
It introduces a dynamic linking process model and uses the rate equation approach to analytically derive properties of evolving random graphs.
Findings
Analytical expressions for links, paths, cycles, and components.
Scaling laws for finite systems derived from extreme statistics.
Dynamic linking process modeled using kinetic theory.
Abstract
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate equation approach. Scaling laws for finite systems are derived using extreme statistics and scaling arguments.
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