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Set-based approximate approach for lossless graph summarization

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Abstract

Graph summarization is valuable approach to analyze various real life phenomenon, like communities, influential nodes, and information flow in a big graph. To summarize a graph, nodes having similar neighbors are merged into super nodes and their corresponding edges are compressed into super edges. Existing methods find similar nodes either by nodes ordering or perform pairwise similarity computations. Compression-by-node ordering approaches are scalable but provide lesser compression due to exhaustive similarity computations of their counterparts. In this paper, we propose a novel set-based summarization approach that directly summarizes naturally occurring sets of similar nodes in a graph. Our approach is scalable since we avoid explicit similarity computations with non-similar nodes and merge sets of nodes in each iteration. Similarly, we provide good compression ratio as each set consists of highly similar nodes. To locate sets of similar nodes, we find candidate sets of similar nodes by using locality sensitive hashing. However, member nodes of every candidate set have varying similarities with each other. Therefore, we propose a heuristic based on similarity among degrees of candidate nodes, and a parameter-free pruning technique to effectively identify subset of highly similar nodes from candidate nodes. Through experiments on real world graphs, our approach requires lesser execution time than pairwise graph summarization, with margin of an order of magnitude in graphs containing nodes with highly diverse neighborhood, and produces summary at similar accuracy. Similarly, we observe comparable scalability against the compression-by-node ordering method, while providing better compression ratio.

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Notes

  1. http://snap.stanford.edu/data/index.html. Last accessed on 10/28/2014.

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Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2014R1A2A1A05043734).

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Authors and Affiliations

  1. Department of Computer Engineering, Kyung Hee University, Seocheon-dong, Giheung-gu, Yongin-si, Gyeonggi-do, 446-701, Republic of Korea

    Kifayat Ullah Khan, Waqas Nawaz & Young-Koo Lee

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  1. Kifayat Ullah Khan
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Correspondence to Young-Koo Lee.

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Khan, K.U., Nawaz, W. & Lee, YK. Set-based approximate approach for lossless graph summarization. Computing 97, 1185–1207 (2015). https://doi.org/10.1007/s00607-015-0454-9

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