Distance Backbones Optimize Spreading Dynamics and Centrality Ranks in the Sparsification of Complex Networks

TL;DR

This paper introduces a novel graph sparsification method called distance backbone synthesis (DBS) that effectively preserves spreading dynamics and node centrality in complex networks by leveraging distance backbones based on generalized triangle inequalities.

Contribution

The paper presents DBS, a principled approach to sparsify weighted graphs while maintaining key properties, and demonstrates its effectiveness on real-world social networks.

Findings

Distance backbones better preserve spreading dynamics.

Optimal sparsification occurs with a specific path-length measure.

Over half of edges can be removed without losing critical network properties.

Abstract

Detailed network models of social, biological and other complex systems are often dense, which increases their computational complexity in simulations and analysis. To address this challenge, graph sparsification is used to remove edges while preserving desired network properties. Distance backbones of weighted graphs, which remove edges that break a generalized triangle inequality for any given path-length measure, preserve all shortest paths of weighted graphs. They have been shown to typically sparsify graphs more, as well as preserve community structure and spreading dynamics better than alternative state-of-the-art methods. Here, We show that they significantly best preserve node centrality ranks, as well as local and global dynamics in spreading phenomena. This is done by introducing the distance backbone synthesis (DBS) to progressively sparsify weighted graphs according to a general family of nested distance backbones, whereby each edge is associated with the smallest distance backbone in which it appears. DBS provides a principled and natural method to sweep all degrees of sparsification possible while preserving connectivity, allowing us to precisely study (directed and undirected) weighted graph sparsification under multi-objective criteria. It provides an algebraically-principled explanation of edge importance by revealing the precise topological space associated with each edge. The theory is demonstrated with a battery of social contact networks obtained from real-world social activity in different scenarios. Our study also shows that the optimal preservation of node centrality and spreading dynamics happens for the distance backbone obeying the generalized triangle inequality for the path-length measure $g(x, y) = (\sqrt[3]{x}+\sqrt[3]{y})^3$, which removes more than half of the edges from the empirical networks studied.