Graph Compression -- Save Information by Exploiting Redundancy

TL;DR

This paper presents a novel approach to compress sparse graphs by exploiting neighbor overlap and symmetry, framing it as an optimization problem and applying a greedy algorithm for effective compression.

Contribution

It introduces a new method for graph compression based on redundancy, neighbor overlap, and symmetry, with a greedy algorithm to optimize the compression process.

Findings

Effective compression achieved through symmetry exploitation

Algorithm demonstrates good performance on example graphs

Redundancy measurement improves compression efficiency

Abstract

In this paper we raise the question of how to compress sparse graphs. By introducing the idea of redundancy, we find a way to measure the overlap of neighbors between nodes in networks. We exploit symmetry and information by making use of the overlap in neighbors and analyzing how information is reduced by shrinking the network and using the specific data structure we created, we generalize the problem of compression as an optimization problem on the possible choices of orbits. To find a reasonably good solution to this problem we use a greedy algorithm to determine the orbit of symmetry identifications, to achieve compression. Some example implementations of our algorithm are illustrated and analyzed.