Reducing Million-Node Graphs to a Few Structural Patterns: A Unified Approach

How do graph clustering techniques compare in terms of summarization power? How well can they summarize a million-node graph with a few representative structures? In this paper, we compare and contrast different techniques: METIS, LOUVAIN, SPECTRAL CLUSTERING, SLASHBURN, BIGCLAM, HYCOMFIT, and KCBC, our proposed k-core-based clustering method. Unlike prior work that focuses on various measures of cluster quality, we use vocabulary structures that often appear in real graphs and the Minimum Description Length (MDL) principle to obtain a graph summary per clustering method. Our main contributions are: (i) Formulation: we propose a summarization-based evaluation of clustering methods. Our method, VOG-OVERLAP, concisely summarizes graphs in terms of their important structures with small edge overlap and large node/edge coverage; (ii) Algorithm: we introduce KCBC, a graph decomposition technique based on the k-core algorithm. We also introduce STEP, a summary assembly heuristic that produces compact summaries, as well as two parallel approximations thereof. (iii) Evaluation: we compare the summarization power of seven clustering techniques on large real graphs and analyze their compression rates, summary statistics, and runtimes.