Multi-relation Graph Summarization

Graph summarization is beneficial in a wide range of applications, such as visualization, interactive and exploratory analysis, approximate query processing, reducing the on-disk storage footprint, graph processing modern hardware. However, bulk literature on surprisingly overlooks possibility having edges different types. In this paper, we study novel problem producing summaries multi-relation networks, i.e., graphs where multiple types may exist between any pair nodes. Multi-relation are an expressive model real-world activities, which relation can be topic social interaction type genetic or snapshot temporal graphs. The first approach that consider for two-step method based summarizing each isolation, then aggregating resulting some clever way to produce final unique summary. doing this, side contribution, provide polynomial-time approximation algorithm k-Median clustering classic lossless single-relation summarization. Then, demonstrate shortcomings these methods, propose holistic approaches, both heuristic algorithms, compute summary directly particular, prove bound single solution maintained with proper aggregation operation over adjacency matrices corresponding its relations. Experimental results case studies (on co-authorship networks brain networks) validate effectiveness efficiency proposed algorithms.