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Discovery of “comet” communities in temporal and labeled graphs Com \(^2\) 

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Abstract

While the analysis of unlabeled networks has been studied extensively in the past, finding patterns in different kinds of labeled graphs is still an open challenge. Given a large edge-labeled network, e.g., a time-evolving network, how can we find interesting patterns? We propose Com \(^2\) , a novel, fast and incremental tensor analysis approach which can discover communities appearing over subsets of the labels. The method is (a) scalable, being linear on the input size, (b) general, (c) needs no user-defined parameters and (d) effective, returning results that agree with intuition. We apply our method to real datasets, including a phone call network, a computer-traffic network and a flight information network. The phone call network consists of 4 million mobile users, with 51 million edges (phone calls), over 14 days, while the flights dataset consists of 7733 airports and 5995 airline companies flying 67,663 different routes. We show that Com \(^2\)  spots intuitive patterns regarding edge labels that carry temporal or other discrete information. Our findings include large “star”-like patterns, near-bipartite cores, as well as tiny groups (five users), calling each other hundreds of times within a few days. We also show that we are able to automatically identify competing airline companies.

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Notes

  1. We tested different methods with no significant differences found in the results since the subsequent steps of growing and shrinking lead to the selection of the most relevant edges and the removal of irrelevant ones. Selecting the edge (i, j, k) with highest \(min(a_i, b_j, c_k)\) provides a good initial seed.

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Acknowledgments

This material is based upon work supported by the National Science Foundation under Grant Nos. IIS-1247489 and IIS-1217559. Research was sponsored by the Defense Threat Reduction Agency and was accomplished under contract No. HDTRA1-10-1-0120 and also sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement No. W911NF-09-2-0053. Additional funding was provided by the US Army Research Office (ARO) and Defense Advanced Research Projects Agency (DARPA) under Contract No. W911NF-11-C-0088. This work is also partially supported by a Google Focused Research Award, by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the Carnegie Mellon Portugal Program under Grant SFRH/BD/52362/2013, by ERDF and FCT through the COMPETE Programme within project FCOMP-01-0124-FEDER-037281 and by a fellowship within the postdoc program of the German Academic Exchange Service (DAAD). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation, DARPA or other funding parties. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on.

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Authors and Affiliations

  1. iLab and School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA

    Miguel Araujo, Stephan Günnemann, Christos Faloutsos, Evangelos E. Papalexakis & Danai Koutra

  2. CRACS/INESC-TEC, University of Porto, Porto, Portugal

    Miguel Araujo

  3. Rutgers University, New Brunswick, NJ, USA

    Spiros Papadimitriou

  4. Raytheon BBN Technologies, Cambridge, MA, USA

    Prithwish Basu

  5. Army Research Laboratory, Adelphi, MD, USA

    Ananthram Swami

  6. Departamento de Ciência de Computadores, Faculdade de Ciências, Universidade do Porto, Porto, Portugal

    Miguel Araujo

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  1. Miguel Araujo
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  2. Stephan Günnemann
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  7. Evangelos E. Papalexakis
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  8. Danai Koutra
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Correspondence to Miguel Araujo.

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Araujo, M., Günnemann, S., Papadimitriou, S. et al. Discovery of “comet” communities in temporal and labeled graphs Com \(^2\) . Knowl Inf Syst 46, 657–677 (2016). https://doi.org/10.1007/s10115-015-0847-2

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  • DOI: https://doi.org/10.1007/s10115-015-0847-2

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