Single- and Multi-level Network Sparsification by Algebraic Distance

TL;DR

This paper introduces a novel network sparsification method based on algebraic distances, capable of preserving structural properties and adaptable to different analysis goals through a multilevel framework.

Contribution

It presents a new algebraic distance-based sparsification technique with a multilevel approach, enhancing control and efficiency in network analysis.

Findings

Effective preservation of structural properties during sparsification

Multilevel framework allows control at various resolutions

Method is easily parallelizable for different architectures

Abstract

Network sparsification methods play an important role in modern network analysis when fast estimation of computationally expensive properties (such as the diameter, centrality indices, and paths) is required. We propose a method of network sparsification that preserves a wide range of structural properties. Depending on the analysis goals, the method allows to distinguish between local and global range edges that can be filtered out during the sparsification. First we rank edges by their algebraic distances and then we sample them. We also introduce a multilevel framework for sparsification that can be used to control the sparsification process at various coarse-grained resolutions. Based primarily on the matrix-vector multiplications, our method is easily parallelized for different architectures.