Communicability Angle and the Spatial Efficiency of Networks

TL;DR

This paper introduces the communicability angle as a new metric for assessing the spatial efficiency of networks, supported by analytical and empirical evidence across diverse real-world systems.

Contribution

It defines the communicability angle, demonstrates its correlation with spatial efficiency, and shows how adjusting edge weights can modulate network efficiency.

Findings

Communicability angle correlates with packing efficiency in protein networks.

The metric effectively characterizes spatial efficiency in various complex networks.

Edge weight tuning can optimize network spatial efficiency.

Abstract

We introduce the concept of communicability angle between a pair of nodes in a graph. We provide strong analytical and empirical evidence that the average communicability angle for a given network accounts for its spatial efficiency on the basis of the communications among the nodes in a network. We determine characteristics of the spatial efficiency of more than a hundred real-world complex networks that represent complex systems arising in a diverse set of scenarios. In particular, we find that the communicability angle correlates very well with the experimentally measured value of the relative packing efficiency of proteins that are represented as residue networks. We finally show how we can modulate the spatial efficiency of a network by tuning the weights of the edges of the networks. This allows us to predict effects of external stresses on the spatial efficiency of a network as well as to design strategies to improve important parameters in real-world complex systems.