# Community-aware network sparsification

## TL;DR

This paper introduces a novel community-aware network sparsification method that preserves community structures, providing algorithms with proven approximation guarantees and demonstrating effectiveness on various datasets.

## Contribution

It formulates a new community-aware sparsification problem, develops approximation algorithms, and validates their effectiveness through extensive experiments.

## Key findings

- Algorithms effectively preserve community structures.
- Proven approximation guarantees for the sparsification algorithms.
- Successful application on diverse datasets.

## Abstract

Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple applications, such as, speeding up graph-mining algorithms, graph visualization, as well as identifying the important network edges. In this paper we consider a novel formulation of the network-sparsification problem. In addition to the network, we also consider as input a set of communities. The goal is to sparsify the network so as to preserve the network structure with respect to the given communities. We introduce two variants of the community-aware sparsification problem, leading to sparsifiers that satisfy different connectedness community properties. From the technical point of view, we prove hardness results and devise effective approximation algorithms. Our experimental results on a large collection of datasets demonstrate the effectiveness of our algorithms.