Abstract
This paper discusses a complete and efficient algorithm for enumerating densely-connected k-Plexes. A k-Plex is a kind of pseudo-clique which imposes a Disconnection Upper Bound (DUB) by the parameter k for each constituent vertex. However, since the parameter is usually fixed not depending on sizes of our targeted pseudo-cliques, we often have k-Plexes not densely-connected. In order to overcome this drawback, we introduce another constraint using a parameter j designating Connection Lower Bound (CLB). Based on CLB, we can additionally enjoy a monotonic j-core operation and design an efficient depth-first algorithm which can exclude hopeless vertex sets which cannot be extended to their supersets satisfying both DUB and CLB. Our experimental results show it can work well as a useful tool for detecting densely-connected pseudo cliques in large networks including one with over 800, 000 vertices.
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The authors of [1] have kindly provided us their program codes of MaxKplexEnum. We would like to sincerely appreciate their kindness.
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Zhai, H., Haraguchi, M., Okubo, Y., Tomita, E. (2016). A Fast and Complete Enumeration of Pseudo-Cliques for Large Graphs. In: Bailey, J., Khan, L., Washio, T., Dobbie, G., Huang, J., Wang, R. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2016. Lecture Notes in Computer Science(), vol 9651. Springer, Cham. https://doi.org/10.1007/978-3-319-31753-3_34
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