An ensemble approach to the analysis of weighted networks

TL;DR

This paper introduces an ensemble-based method for calculating network measures in weighted networks, enabling straightforward generalizations of unweighted network metrics and demonstrating its effectiveness on real-world data.

Contribution

The paper proposes a novel ensemble approach to extend unweighted network measures to weighted networks, simplifying their calculation and interpretation.

Findings

Enables direct generalization of unweighted measures to weighted networks

Demonstrates improved clustering coefficient calculation on real-world networks

Provides a versatile framework applicable to various network metrics

Abstract

We present a new approach to the calculation of measures in weighted networks, based on the translation of a weighted network into an ensemble of edges. This leads to a straightforward generalization of any measure defined on unweighted networks, such as the average degree of the nearest neighbours, the clustering coefficient, the `betweenness', the distance between two nodes and the diameter of a network. All these measures are well established for unweighted networks but have hitherto proven difficult to define for weighted networks. Further to introducing this approach we demonstrate its advantages by applying the clustering coefficient constructed in this way to two real-world weighted networks.