Random graphs containing arbitrary distributions of subgraphs

TL;DR

This paper introduces a new class of random graph models that incorporate arbitrary subgraphs, capturing more realistic non-tree-like local structures in networks while remaining analytically tractable.

Contribution

It proposes and analyzes a novel random graph model that includes general subgraphs, enabling realistic modeling of networks with complex local neighborhoods.

Findings

Derived solutions for the size of the giant component

Identified the phase transition point for giant component emergence

Analyzed percolation properties for site and bond percolation

Abstract

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly non-tree-like neighborhoods that contain short loops, cliques, or other biconnected subgraphs. In this paper we propose and analyze a new class of random graph models that incorporates general subgraphs, allowing for non-tree-like neighborhoods while still remaining solvable for many fundamental network properties. Among other things we give solutions for the size of the giant component, the position of the phase transition at which the giant component appears, and percolation properties for both site and bond percolation on networks generated by the model.