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

2026-03-15

AI Summary

This study addresses the high computational complexity of dense, complex networks by proposing an effective sparsification method that preserves essential structural and dynamical properties. The authors introduce the Distance Backbone Synthesis (DBS) framework, which sparsifies weighted graphs based on a generalized triangle inequality, rigorously maintaining all shortest paths while assigning each edge its minimal backbone level—the earliest layer at which it appears—thereby offering an algebraically interpretable measure of edge importance. Theoretical analysis and multi-objective optimization demonstrate that under the path-length metric $g(x, y) = (\sqrt[3]{x} + \sqrt[3]{y})^3$, DBS removes over 50% of redundant edges. In empirical evaluations on real-world social contact networks, DBS significantly outperforms existing methods, simultaneously achieving optimal preservation of node centrality rankings and both local and global spreading dynamics.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Social Networks and Social Media: Computational social science

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.

Problem

• graph sparsification
• complex networks
• distance backbone
• centrality preservation
• spreading dynamics

Innovation

• distance backbone
• graph sparsification
• spreading dynamics
• centrality preservation
• triangle inequality