Gromov Centrality: A Multi-Scale Measure of Network Centrality Using Triangle Inequality Excess

TL;DR

Gromov centrality is a multi-scale network importance measure based on triangle inequality excess, capturing geometric properties and boundary effects to distinguish node roles across different scales.

Contribution

This paper introduces Gromov centrality, a novel multi-scale centrality measure using triangle inequality excess to analyze network importance from a geometric perspective.

Findings

Gromov centrality recovers known measures like clustering coefficient and closeness centrality as special cases.

It effectively distinguishes node types in random geometric graphs and transportation networks.

The measure is influenced by geometric and boundary constraints of the network.

Abstract

Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multi-scale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and recovers as limits well-known concept such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks.