Abstract
Counts of small subgraphs, or graphlet counts, are widely applicable to measure graph similarity. Computing graphlet counts can be computationally expensive and may pose obstacles in network analysis. We study the role of cliques in graphlet counts as a method for graph similarity in social networks. Higher-order clustering coefficients and the Pivoter algorithm for exact clique counts are employed.
Research supported by a grant of the first author from NSERC.
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References
Ashford, J.R., Turner, L.D., Whitaker, R.M., Preece, A., Felmlee, D.: Understanding the characteristics of COVID-19 misinformation communities through graphlet analysis. Online Soc. Networks Media 27, 100178 (2022)
D’Angelo, D.R., Bonato, A., Elenberg, E.R., Gleich, D.F., Hou, Y.: Mining and modeling character networks. In: Proceedings of Algorithms and Models for the Web Graph (2016)
Bonato, A.: A Course on the Web Graph. American Mathematical Society, Providence, Rhode Island (2008)
Bonato, A., Cushman, R., Marbach, T., Zhang, Z.: An evolving network model from clique extension. In: Proceedings of the 28th International Computing and Combinatorics Conference (2022)
Bonato, A., Eikmeier, N., Gleich, D.F., Malik, R.: Centrality in dynamic competition networks. In: Proceedings of Complex Networks (2019)
Bonato, A., et al.: Dimensionality matching of social networks using motifs and eigenvalues. PLoS ONE 9(9), e106052 (2014)
Borgwardt, K., Ghisu, E., Llinares-López, F., O’Bray, L., Rieck, B.: Graph kernels: state-of-the-art and future challenges. Found. Trends Mach. Learn. 13, 531–712 (2020)
Feng, B., et al.: Motif importance measurement based on multi-attribute decision. J. Complex Networks 10, cnac023 (2022)
Fox, J., Roughgarden, T., Seshadhri, C., Wei, F., Wein, N.: Finding cliques in social networks: a new distribution-free model. SIAM J. Comput. 49, 448–464 (2020)
Jain, S., Seshadhri, C.: The power of pivoting for exact clique counting. In: Proceedings of the 13th International Conference on Web Search and Data Mining (2020)
Janssen, J., Hurshman, M., Kalyaniwalla, N.: Model selection for social networks using graphlets. Internet Math. 8, 338–363 (2012)
Lawford, S., Mehmeti, Y.: Cliques and a new measure of clustering: with application to US domestic airlines. Phys. A 560, 125158 (2020)
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceedings of the Eleventh ACM SIGKDD International Conference on Knowledge Discovery in Data Mining (2005)
Leskovec, J., Krevl, A.: SNAP datasets: stanford large network dataset collection (2014). http://snap.stanford.edu/data
Milo, R., Shen-Orr, R.S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002)
Morris, C., Kriege, N.M., Bause, F., Kersting, K., Mutzel, P., Neumann, M.: TUDataset: a collection of benchmark datasets for learning with graphs. In: Proceedings of ICML 2020 Workshop on Graph Representation Learning and Beyond (2020)
Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)
Pi, H., Burghardt, K., Percus, A.G., Lerman, K.: Clique densification in networks. Phys. Rev. E 107, L042301 (2023)
Pržulj, N.: Biological network comparison using graphlet degree distribution. Bioinformatics 23, e177–e183 (2007)
Ribeiro, P., Paredes, P., Silva, M., Aparicio, D., Silva, F.: A survey on subgraph counting: concepts, algorithms, and applications to network motifs and graphlets. ACM Comput. Surv. 54, 1–36 (2021)
Rozemberczki, B., Kiss, O., Sarkar, R.: Karate Club: an API oriented open-source Python framework for unsupervised learning on graphs. In: Proceedings of the 29th ACM International Conference on Information and Knowledge Management (2020)
Shervashidze, N., Vishwanathan, S.V.N., Petri, T., Mehlhorn, K., Borgwardt, K.: Efficient graphlet kernels for large graph comparison. In: Proceedings of the Twelth International Conference on Artificial Intelligence and Statistics, pp. 488–495 (2009)
Sinha, S., Bhattacharya, S., Roy, S.: Impact of second-order network motif on online social networks. J. Supercomput. 78, 5450–5478 (2022)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)
West, D.B.: Introduction to Graph Theory, 2nd edition. Prentice Hall (2001)
Yanardag, P., Vishwanathan, S.V.N.: Deep graph kernels. In: Proceedings of the 21st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2015)
Yin, H., Benson, A.R., Leskovec, J.: Higher-order clustering in networks. Phys. Rev. E 97, 052306 (2018)
Zhao, H., Shao, C., Shi, Z., He, S., Gong, Z.: The intrinsic similarity of topological structure in biological neural networks. IEEE/ACM Trans. Comput. Biol. Bioinf. 20, 3292–3305 (2023)
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Bonato, A., Zhang, Z. (2024). Clique Counts for Network Similarity. In: Dewar, M., et al. Modelling and Mining Networks. WAW 2024. Lecture Notes in Computer Science, vol 14671. Springer, Cham. https://doi.org/10.1007/978-3-031-59205-8_12
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