How modular structure can simplify tasks on networks

TL;DR

This paper introduces a novel algorithm for shortest walk problems that leverages network modularity, significantly reducing computational complexity by focusing on dense regions identified through local community detection.

Contribution

The work presents a new algorithm that exploits modular structure to simplify network tasks, supporting heuristic detection of dense regions to accelerate optimization.

Findings

Algorithm scales with coarsened network size rather than total nodes

Preprocessing with local community detection improves efficiency

Supports conjectures on structural scaling in networked systems

Abstract

By considering the task of finding the shortest walk through a network we find an algorithm for which the run time is not as O(2^n), with n being the number of nodes, but instead scales with the number of nodes in a coarsened network. This coarsened network has a number of nodes related to the number of dense regions in the original graph. Since we exploit a form of local community detection as a preprocessing, this work gives support to the project of developing heuristic algorithms for detecting dense regions in networks: preprocessing of this kind can accelerate optimization tasks on networks. Our work also suggests a class of empirical conjectures for how structural features of efficient networked systems might scale with system size.