Graph space: using both geometric and probabilistic structure to evaluate statistical graph models

TL;DR

This paper introduces the EDEV metric combining geometric and probabilistic graph structures to evaluate statistical graph models, enabling better distinction of typical versus atypical graphs and providing a hypothesis testing framework.

Contribution

The paper proposes the EDEV metric that integrates geometric and probabilistic information for graph model evaluation, improving discrimination capabilities.

Findings

EDEV outperforms entropy and barycenter distance in distinguishing graph structures.

EDEV effectively identifies graphs consistent with a given statistical model.

A hypothesis testing method based on EDEV assesses model relevance to observed graphs.

Abstract

Statistical graph models aim at modeling graphs as random realization among a set of possible graphs. One issue is to evaluate whether or not a graph is likely to have been generated by one particular model. In this paper we introduce the edit distance expected value (EDEV) and compare it with other methods such as entropy and distance to the barycenter. We show that contrary to them, EDEV is able to distinguish between graphs that have a typical structure with respect to a model, and those that do not. Finally we introduce a statistical hypothesis testing methodology based on this distance to evaluate the relevance of a candidate model with respect to an observed graph.