Analysis of weighted networks

TL;DR

This paper demonstrates that weighted networks can be effectively analyzed by mapping them to unweighted multigraphs, enabling the use of standard graph techniques for weighted network analysis.

Contribution

It introduces a simple method to analyze weighted networks using unweighted graph techniques and provides applications like community detection and a proof of max-flow/min-cut.

Findings

Weighted networks can be mapped to unweighted multigraphs.

The method allows applying standard unweighted graph algorithms to weighted networks.

Examples include community detection and a new proof of max-flow/min-cut.

Abstract

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.