Random Graph Models with Hidden Color

TL;DR

This paper introduces a generalized framework for random graph models using hidden, unobservable vertex or stub attributes called colors, enabling complex correlation structures and broadening the scope of graph modeling.

Contribution

It presents a unifying formalism for extending classic random graph models with hidden color variables that influence edge probabilities and correlations.

Findings

Provides a flexible method to incorporate hidden attributes in graph models.

Enables modeling of complex edge correlation structures.

Unifies various random graph models under a common framework.

Abstract

We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom, color, applied to vertices or stubs (half-edges). The color is assumed unobservable, but is allowed to affect edge probabilities. This serves as a convenient method to define very general classes of models within a common unifying formalism, and allowing for a non-trivial edge correlation structure.