Normal and stable approximation to subgraph counts in superpositions of Bernoulli random graphs

TL;DR

This paper develops normal and stable distribution approximations for counting small subgraphs like cliques and cycles in complex networks modeled as superpositions of Bernoulli graphs, capturing clustering and degree distribution features.

Contribution

It introduces new probabilistic approximations for subgraph counts in superimposed Bernoulli graph models with realistic network properties.

Findings

Normal approximation for subgraph counts in large networks

Stable distribution approximation for heavy-tailed degree distributions

Quantitative bounds on approximation accuracy

Abstract

The clustering property of complex networks indicates the abundance of small dense subgraphs in otherwise sparse networks. For a community-affiliation network defined by a superposition of Bernoulli random graphs, which has a nonvanishing global clustering coefficient and a power-law degree distribution, we establish normal and $\alpha$--stable approximations to the number of small cliques, cycles and more general $2$-connected subgraphs.