Graph Summarization via Node Grouping: A Spectral Algorithm

TL;DR

This paper introduces SpecSumm, a spectral algorithm for graph summarization via node grouping, which efficiently produces high-quality summaries by leveraging spectral properties and clustering techniques, scalable to large graphs.

Contribution

The paper reformulates graph summarization as an integer maximization problem and develops a spectral clustering-based algorithm with a greedy heuristic for improved summaries.

Findings

SpecSumm outperforms existing algorithms in summary quality.

It scales efficiently to graphs with millions of nodes.

Experimental results on 11 datasets validate its effectiveness.

Abstract

Graph summarization via node grouping is a popular method to build concise graph representations by grouping nodes from the original graph into supernodes and encoding edges into superedges such that the loss of adjacency information is minimized. Such summaries have immense applications in large-scale graph analytics due to their small size and high query processing efficiency. In this paper, we reformulate the loss minimization problem for summarization into an equivalent integer maximization problem. By initially allowing relaxed (fractional) solutions for integer maximization, we analytically expose the underlying connections to the spectral properties of the adjacency matrix. Consequently, we design an algorithm called SpecSumm that consists of two phases. In the first phase, motivated by spectral graph theory, we apply k-means clustering on the k largest (in magnitude) eigenvectors of the adjacency matrix to assign nodes to supernodes. In the second phase, we propose a greedy heuristic that updates the initial assignment to further improve summary quality. Finally, via extensive experiments on 11 datasets, we show that SpecSumm efficiently produces high-quality summaries compared to state-of-the-art summarization algorithms and scales to graphs with millions of nodes.