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Given a terabyte-scale graph distributed across multiple machines, how can we summarize it, with much fewer nodes and edges, so that we can restore the original graph exactly or within error bounds?As large-scale graphs are ubiquitous, ranging from web graphs to online social networks, compactly representing graphs becomes important to efficiently store and process them. Given a graph, graph summarization aims to find its compact representation consisting of (a) a summary graph where the nodes are disjoint sets of nodes in the input graph, and each edge indicates the edges between all pairs of nodes in the two sets; and (b) edge corrections for restoring the input graph from the summary graph exactly or within error bounds. Although graph summarization is a widely-used graph-compression technique readily combinable with other techniques, existing algorithms for graph summarization are not satisfactory in terms of speed or compactness of outputs. More importantly, they assume that the input graph is small enough to fit in main memory. In this work, we propose SWeG, a fast parallel algorithm for summarizing graphs with compact representations. SWeG is designed for not only shared-memory but also MapReduce settings to summarize graphs that are too large to fit in main memory. We demonstrate that SWeG is (a) Fast: SWeG is up to 5400 × faster than its competitors that give similarly compact representations, (b) Scalable: SWeG scales to graphs with tens of billions of edges, and (c) Compact: combined with state-of-the-art compression methods, SWeG achieves up to 3.4 × better compression than them.

SWeG: Lossless and Lossy Summarization of Web-Scale Graphs