Extracting the multiscale backbone of complex weighted networks

TL;DR

This paper introduces a new filtering method for extracting the multiscale backbone of weighted networks, effectively identifying significant connections across all scales without bias towards large interactions.

Contribution

The authors propose a novel statistical filtering technique that preserves multiscale interactions in complex weighted networks, outperforming existing methods in relevance and scale-invariance.

Findings

The method successfully extracts meaningful backbones from real-world networks.

It maintains small-scale interactions often overlooked by other techniques.

Compared to alternatives, it better captures the multiscale structure of networks.

Abstract

A large number of complex systems find a natural abstraction in the form of weighted networks whose nodes represent the elements of the system and the weighted edges identify the presence of an interaction and its relative strength. In recent years, the study of an increasing number of large scale networks has highlighted the statistical heterogeneity of their interaction pattern, with degree and weight distributions which vary over many orders of magnitude. These features, along with the large number of elements and links, make the extraction of the truly relevant connections forming the network's backbone a very challenging problem. More specifically, coarse-graining approaches and filtering techniques are at struggle with the multiscale nature of large scale systems. Here we define a filtering method that offers a practical procedure to extract the relevant connection backbone in complex multiscale networks, preserving the edges that represent statistical significant deviations with respect to a null model for the local assignment of weights to edges. An important aspect of the method is that it does not belittle small-scale interactions and operates at all scales defined by the weight distribution. We apply our method to real world network instances and compare the obtained results with alternative backbone extraction techniques.