Abstract
The paper presents the results of correlation analysis between node centrality (a computationally lightweight metric) and the maximal clique size (a computationally hard metric) that each node is part of in complex real-world network graphs, ranging from regular random graphs to scale-free graphs. The maximal clique size for a node is the size of the largest clique (number of constituent nodes) the node is part of. The correlation coefficient between the centrality value and the maximal clique size for a node is observed to increase with increase in the spectral radius ratio for node degree (a measure of the variation of node degree in the network). As the real-world networks get increasingly scale-free, the correlation between the centrality value and the maximal clique size increases. The degree-based centrality metrics are observed to be relatively better correlated with the maximal clique size compared to the shortest path-based centrality metrics.
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References
Newman, M.: Networks: An Introduction, 1st edn. Oxford University Press, Oxford (2010)
Strang, G.: Linear Algebra and its Applications, 1st edn. Cengage Learning, Boston (2005)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)
Brandes, U.: A faster algorithm for betweenness centrality. J. Math. Sociol. 25, 163–177 (2001)
Pattabiraman, B., Patwary, M.A., Gebremedhin, A.H., Liao, W.-K., Choudhary, A.: Fast algorithms for the maximum clique problem on massive sparse graphs. In: Bonato, A., Mitzenmacher, M., Pralat, P. (eds.): 10th International Workshop on Algorithms and Models for the Web Graph. Lecture Notes in Computer Science, vol. 8305, pp. 156–169. Springer-Verlag, Berlin Heidelberg New York (2013)
Fortunato, S.: Community detection in graphs. Phys. Rep. 486, 75–174 (2010)
Palla, G., Derenyi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435, 814–818 (2005)
Sadi, S., Oguducu, S., Uyar, A.S.: An efficient community detection method using parallel clique-finding ants. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1–7. IEEE, Piscataway NJ (2010)
Tomita, E., Kameda, T.: An efficient branch-and-bound algorithm for finding a maximum clique with computational experiments. J. Global Optim. 37, 95–11 (2007)
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Meghanathan, N. (2016). Maximal Clique Size Versus Centrality: A Correlation Analysis for Complex Real-World Network Graphs. In: Nagar, A., Mohapatra, D., Chaki, N. (eds) Proceedings of 3rd International Conference on Advanced Computing, Networking and Informatics. Smart Innovation, Systems and Technologies, vol 44. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2529-4_9
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DOI: https://doi.org/10.1007/978-81-322-2529-4_9
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