Network Sparsification via Degree- and Subgraph-based Edge Sampling

TL;DR

This paper introduces a novel network sparsification method based on local node properties like degrees, wedges, and triangles, which preserves structural features more effectively than traditional filtering-based sampling.

Contribution

It proposes a generalized local-property-based sampling approach that maintains key node characteristics, improving structural preservation in graph sparsification.

Findings

Preserves complex network structures effectively

Achieves at least 4 times faster convergence

Demonstrates superior performance on climate networks

Abstract

Network (or graph) sparsification compresses a graph by removing inessential edges. By reducing the data volume, it accelerates or even facilitates many downstream analyses. Still, the accuracy of many sparsification methods, with filtering-based edge sampling being the most typical one, heavily relies on an appropriate definition of edge importance. Instead, we propose a different perspective with a generalized local-property-based sampling method, which preserves (scaled) local \emph{node} characteristics. Apart from degrees, these local node characteristics we use are the expected (scaled) number of wedges and triangles a node belongs to. Through such a preservation, main complex structural properties are preserved implicitly. We adapt a game-theoretic framework from uncertain graph sampling by including a threshold for faster convergence (at least $4$ times faster empirically) to approximate solutions. Extensive experimental studies on functional climate networks show the effectiveness of this method in preserving macroscopic to mesoscopic and microscopic network structural properties.