Exposure theory for learning complex networks with random walks

TL;DR

This paper introduces exposure theory, a statistical mechanics framework that accurately predicts how random walks explore complex networks, including weighted and temporal types, revealing universal patterns in edge discovery.

Contribution

The paper presents a novel exposure theory that models and predicts network exploration dynamics of random walks across various network types, including weighted and temporal networks.

Findings

Edge learning follows a universal trajectory.

Exposure theory accurately predicts aggregate exploration statistics.

The framework applies to weighted and temporal networks.

Abstract

Random walks are a common model for exploration and discovery of complex networks. While numerous algorithms have been proposed to map out an unknown network, a complementary question arises: in a known network, which nodes and edges are most likely to be discovered by a random walker in finite time? Here we introduce exposure theory, a statistical mechanics framework that predicts the learning of nodes and edges across several types of networks, including weighted and temporal, and show that edge learning follows a universal trajectory. While the learning of individual nodes and edges is noisy, exposure theory produces a highly accurate prediction of aggregate exploration statistics.