Random Graphs with Hidden Color

TL;DR

This paper introduces a new class of sparse random graph models with hidden coloring, unifying existing models and enabling analytical calculation of graph properties like component sizes and percolation thresholds.

Contribution

It presents a unifying formalism for random graphs with hidden colors, extending previous models and allowing for detailed analytical insights into their structure.

Findings

Derived size distribution of connected components

Identified percolation threshold for giant component

Unified multiple random graph ensembles

Abstract

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a nontrivial correlation structure in the resulting graphs. The approach unifies a number of existing random graph ensembles within a common general formalism, and allows for the analytic calculation of observable graph characteristics. In particular, generating function techniques are used to derive the size distribution of connected components (clusters) as well as the location of the percolation threshold where a giant component appears.