Graph Summarization via Node Grouping: A Spectral Algorithm
This work addresses the need for concise graph representations to improve query processing efficiency in large-scale graph analytics, representing an incremental advancement over existing methods.
The paper tackles the problem of graph summarization via node grouping by reformulating it as an integer maximization problem and designing a spectral algorithm called SpecSumm, which efficiently produces high-quality summaries and scales to graphs with millions of nodes, as shown in experiments on 11 datasets.
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.