The hidden geometry of weighted complex networks

TL;DR

This paper provides empirical evidence that weighted complex networks can be understood through hidden geometric spaces, revealing insights into their topology, weights, and evolution, with implications for various scientific fields.

Contribution

It introduces a versatile model that captures the coupling between network topology, weights, and underlying geometry, advancing understanding of weighted complex networks.

Findings

The geometric interpretation applies to weighted networks.

The model accurately reproduces network topology and weights.

Connections and weight assignments are governed by different processes.

Abstract

The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of their complex topologies, this hypothesis yields the recipe for sustainable Internet's routing protocols, sheds light on the hierarchical organization of biochemical pathways in cells, and allows for a rich characterization of the evolution of international trade. We present empirical evidence that this geometric interpretation also applies to the weighted organisation of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights, and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.