Summarizing Labeled Multi-Graphs

TL;DR

This paper introduces LM-Gsum, a novel graph summarization method capable of handling complex, labeled, directed, and multi-edged graphs, effectively simplifying visualization while preserving high-level structure and achieving efficient compression.

Contribution

LM-Gsum is the first comprehensive model to summarize multi-characteristic graphs, capturing key sub-structures and optimizing encoding for lossless reconstruction with improved efficiency.

Findings

Facilitates visualization of complex real-world graphs.

Achieves better compression and runtime trade-offs.

Effectively captures important sub-structures like cliques and stars.

Abstract

Real-world graphs can be difficult to interpret and visualize beyond a certain size. To address this issue, graph summarization aims to simplify and shrink a graph, while maintaining its high-level structure and characteristics. Most summarization methods are designed for homogeneous, undirected, simple graphs; however, many real-world graphs are ornate; with characteristics including node labels, directed edges, edge multiplicities, and self-loops. In this paper we propose LM-Gsum, a versatile yet rigorous graph summarization model that (to the best of our knowledge, for the first time) can handle graphs with all the aforementioned characteristics (and any combination thereof). Moreover, our proposed model captures basic sub-structures that are prevalent in real-world graphs, such as cliques, stars, etc. LM-Gsum compactly quantifies the information content of a complex graph using a novel encoding scheme, where it seeks to minimize the total number of bits required to encode (i) the summary graph, as well as (ii) the corrections required for reconstructing the input graph losslessly. To accelerate the summary construction, it creates super-nodes efficiently by merging nodes in groups. Experiments demonstrate that LM-Gsum facilitates the visualization of real-world complex graphs, revealing interpretable structures and high- level relationships. Furthermore, LM-Gsum achieves better trade-off between compression rate and running time, relative to existing methods (only) on comparable settings.