Graph Model Selection via Random Walks

TL;DR

This paper introduces a random walk-based method for graph model selection that produces invariant, discriminative features capable of distinguishing complex graph models efficiently.

Contribution

It proposes a novel random walk approach that captures structural signatures of graphs, enabling scalable and invariant model discrimination.

Findings

Achieves near-theoretical performance in model discrimination tasks

Provides a scalable and simple computational method

Successfully distinguishes complex graph models in experiments

Abstract

In this paper, we present a novel approach based on the random walk process for finding meaningful representations of a graph model. Our approach leverages the transient behavior of many short random walks with novel initialization mechanisms to generate model discriminative features. These features are able to capture a more comprehensive structural signature of the underlying graph model. The resulting representation is invariant to both node permutation and the size of the graph, allowing direct comparison between large classes of graphs. We test our approach on two challenging model selection problems: the discrimination in the sparse regime of an Erd\"{o}s-Renyi model from a stochastic block model and the planted clique problem. Our representation approach achieves performance that closely matches known theoretical limits in addition to being computationally simple and scalable to large graphs.