Abstract
A core in a graph is usually taken as a set of highly connected vertices. Although general, this definition is intuitive and useful for studying the structure of many real networks. Nevertheless, depending on the problem, different formulations of graph core may be required, leading us to the known concept of generalized core. In this paper we study and further extend the notion of generalized core. Given a graph, we propose a definition of graph core based on a subset of its subgraphs and on a subgraph property function. Our approach generalizes several notions of graph core proposed independently in the literature, introducing a general and theoretical sound framework for the study of fully generalized graph cores. Moreover, we discuss emerging applications of graph cores, such as improved graph clustering methods and complex network motif detection.
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References
Seidman, S.B.: Network structure and minimum degree. Social Networks 5(3), 269–287 (1983)
Wasserman, S., Faust, K.: Social network analysis: Methods and applications. Cambridge University Press, Cambridge (1994)
Batagelj, V., Zaveršnik, M.: Generalized cores. arXiv:cs/0202039 (2002)
Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: Natural cluster sizes and the absence of large well-define clusters. arXiv:0810.1355 (2008)
Wei, F., Qian, W., Wang, C., Zhou, A.: Detecting Overlapping Community Structures in Networks. World Wide Web 12(2), 235–261 (2009)
Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high-performance scientific simulations. Morgan Kaufmann Publishers, Inc., San Francisco (2003)
Abou-Rjeili, A., Karypis, G.: Multilevel algorithms for partitioning power-law graphs. In: IEEE International Parallel & Distributed Processing Symposium, p. 10. IEEE, Los Alamitos (2006)
Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)
Farkas, I., Ábel, D., Palla, G., Vicsek, T.: Weighted network modules. New J. Physics 9(6), 180 (2007)
Shen, H., Cheng, X., Cai, K., Hu, M.B.: Detect overlapping and hierarchical community structure in networks. Physica A: Statistical Mechanics and its Applications 388(8), 1706–1712 (2009)
Saito, K., Yamada, T., Kazama, K.: Extracting Communities from Complex Networks by the k-dense Method. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences 91, 3304–3311 (2008)
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network Motifs: Simple Building Blocks of Ccomplex Networks. Science 298, 824–827 (2002)
Saito, R., Suzuki, H., Hayashizaki, Y.: Construction of reliable protein-protein interaction networks with a new interaction generality measure. Bioinformatics 19(6), 756–763 (2002)
Albert, I., Albert, R.: Conserved network motifs allow protein-protein interaction prediction. Bioinformatics 20(18), 3346–3352 (2004)
Kashtan, N., Itzkovitz, S., Milo, R., Alon, U.: Efficient sampling algorithm for estimating subgraph concentrations and detecting network motifs. Bioinformatics 20(11), 1746–1758 (2004)
Kuramochi, M., Karypis, G.: An efficient algorithm for discovering frequent subgraphs. IEEE Transactions on Knowledge and Data Engineering 16(9), 1038–1051 (2004)
Milenković, T., Lai, J., Pržulj, N.: Graphcrunch: a tool for large network analyses. BMC Bioinformatics 9(1), 70 (2008)
Jaccard, P.: Distribution de la flore alpine dans le Bassin des Dranses et dans quelques regions voisines. Bull. Soc. Vaud. Sci. Nat. 37, 241–272 (1901)
Tanimoto, T.T.: IBM Internal Report November 17th. Technical report, IBM (1957)
Xu, X., Yuruk, N., Feng, Z., Schweiger, T.A.J.: Scan: a structural clustering algorithm for networks. In: SIGKDD, pp. 824–833. ACM, New York (2007)
Whitney, H.: On the abstract properties of linear dependence. American Journal of Mathematics 57(3), 509–533 (1935)
Tutte, W.T.: Lectures on matroids. J. Res. Nat. Bur. Stand. B 69, 1–47 (1965)
Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the AMS 7(1), 48–50 (1956)
Borůvka, O.: On a minimal problem. Prace Moraské Pridovedecké Spolecnosti 3 (1926)
Spielman, D.A., Teng, S.H.: A local clustering algorithm for massive graphs and its application to nearly-linear time graph partitioning. arXiv.org:0809.3232 (2008)
Andersen, R., Lang, K.J.: Communities from seed sets. In: WWW, pp. 223–232. ACM, New York (2006)
Chung, F.: The heat kernel as the pagerank of a graph. PNAS 104(50), 19735–19740 (2007)
Lancichinetti, A., Fortunato, S., Kertész, J.: Detecting the overlapping and hierarchical community structure in complex networks. New J. Physics 11, 33015 (2009)
Blondel, V.D., Guillaume, J.L., Lambiotte, R., Lefebvre, E.: Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 10008 (2008)
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Francisco, A.P., Oliveira, A.L. (2011). Fully Generalized Graph Cores. In: da F. Costa, L., Evsukoff, A., Mangioni, G., Menezes, R. (eds) Complex Networks. Communications in Computer and Information Science, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25501-4_3
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DOI: https://doi.org/10.1007/978-3-642-25501-4_3
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