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Focus statistics for testing network centrality on uncorrelated random graphs

Published online by Cambridge University Press:  28 December 2016

TAI-CHI WANG  and
FREDERICK KIN HING PHOA
TAI-CHI WANG
Affiliation:
National Center for High-Performance Computing, Hsinchu City 300, Taiwan (e-mail: taichi43@stat.sinica.edu.tw)
FREDERICK KIN HING PHOA
Affiliation:
Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan (e-mail: fredphoa@stat.sinica.edu.tw)
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Abstract

Network centrality has been addressed for more than 30 years; however, few studies provided statistical tests for verifying this network characteristic. By applying the idea of focus test in spatial analysis, we propose a statistical method to test the centrality of a network. We consider not only the degree of node, but also give weights on other nodes with different lengths of the shortest paths, which are called “distances” in networks. According to the density of distance based on the hidden variable model and the property of the multinomial distribution, a test statistic called “focus centrality” is provided to evaluate a network centrality. Besides the theoretical construction, we verify that the proposed method is feasible and effective in the simulation studies. Further, two empirical network data are studied as demonstrations.

Keywords

network centralityfocus centralitydensity of distancemultinomial distributionuncorrelated random graph
Type
Research Article
Information
Network Science , Volume 4 , Issue 4 , December 2016 , pp. 460 - 473
Copyright
Copyright © Cambridge University Press 2016 

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References

Bauckhage, C., Kersting, K., & Rastegarpanah, B. (2013). The Weibull as a model of shortest path distributions in random networks. In Proceedings of the international workshop on mining and learning with graphs. Chicago, IL, USA.Google Scholar
Beebe, N. H. F. (2002). Nelson hf beebes bibliographies page. Retrieved from http://www.math.utah.edu/~beebe/bibliographies.html, 16.Google Scholar
Blondel, V. D., Guillaume, J.-L., Hendrickx, J. M., & Jungers, R. M. (2007). Distance distribution in random graphs and application to network exploration. Physical Review E, 76 (6), 066101.Google Scholar
Boguná, M., & Pastor-Satorras, R. (2003). Class of correlated random networks with hidden variables. Physical Review E, 68 (3), 036112.Google Scholar
Bonacich, P. (1972). Factoring and weighting approaches to status scores and clique identification. Journal of Mathematical Sociology, 2 (1), 113–120.Google Scholar
Bonacich, P. (1987). Power and centrality: A family of measures. American Journal of Sociology, 92 (5), 1170–1182.Google Scholar
Borgatti, S. P., & Everett, M. G. (2006). A graph-theoretic perspective on centrality. Social Networks, 28 (4), 466–484.CrossRefGoogle Scholar
Catanzaro, M., Boguñá, M., & Pastor-Satorras, R. (2005). Generation of uncorrelated random scale-free networks. Physical Review E, 71 (2), 027103.Google Scholar
Erdős, P., & Rényi, A. (1959). On random graphs. Publicationes Mathematicae Debrecen, 6, 290–297.Google Scholar
Frank, O. (2002). Using centrality modeling in network surveys. Social Networks, 24 (4), 385–394.Google Scholar
Freeman, L. C. (1979). Centrality in social networks conceptual clarification. Social networks, 1 (3), 215–239.Google Scholar
Friedkin, N. E. (1991). Theoretical foundations for centrality measures. American Journal of Sociology, 96 (6), 1478–1504.Google Scholar
Fronczak, A., Fronczak, P., & Hołyst, J. A. (2004). Average path length in random networks. Physical Review E, 70 (5), 056110.Google Scholar
Handcock, M. S., Raftery, A. E., & Tantrum, J. M. (2007). Model-based clustering for social networks. Journal of the Royal Statistical Society: Series A (Statistics in Society), 170 (2), 301–354.Google Scholar
Heard, N. A., Weston, D. J., Platanioti, K., & Hand, D. J. (2010). Bayesian anomaly detection methods for social networks. The Annals of Applied Statistics, 4 (2), 645–662.Google Scholar
Hunter, D. R., Goodreau, S. M., & Handcock, M. S. (2008). Goodness of fit of social network models. Journal of the American Statistical Association, 103 (481), 248–258.Google Scholar
Kulldorff, M. (1997). A spatial scan statistic. Communications in Statistics–Theory and Methods, 26 (6), 1481–1496.CrossRefGoogle Scholar
Newman, M. E. J. (2005). A measure of betweenness centrality based on random walks. Social Networks, 27 (1), 39–54.Google Scholar
Newman, M. E. J., & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69 (2), 026113.Google Scholar
Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2001). Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64 (2), 026118.CrossRefGoogle ScholarPubMed
Opsahl, T., Agneessens, F., & Skvoretz, J. (2010). Node centrality in weighted networks: Generalizing degree and shortest paths. Social Networks, 32 (3), 245–251.Google Scholar
Robins, G., & Daraganova, G. (2012). Social selection, dyadic covariates, and geospatial effects. In Lusher, D., Koskinen, J., & Robins, G. (Eds.), Exponential random graph models for social networks: Theory, methods and applications (pp. 91–101). Cambridge: Cambridge University Press.Google Scholar
Robins, G., Pattison, P., Kalish, Y. & Lusher, D. (2007). An introduction to exponential random graph (p*) models for social networks. Social Networks, 29 (2), 173–191.Google Scholar
Tango, T. (2002). Score tests for detecting excess risks around putative sources. Statistics in Medicine, 21 (4), 497–514.Google Scholar
Waller, L. A., & Lawson, A. B. (1995). The power of focused tests to detect disease clustering. Statistics in Medicine, 14 (21–22), 2291–2308.Google Scholar
Wang, T.-C., & Phoa, F. K. H. (2016). A scanning method for detecting clustering pattern of both attribute and structure in social networks. Physica A: Statistical Mechanics and its Applications, 445, 295–309.CrossRefGoogle Scholar
Wasserman, L. (2004). All of statistics: a concise course in statistical inference. New York, NY: Springer.Google Scholar
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of small-world networks. Nature, 393 (6684), 440–442.Google Scholar
Wong, L. H., Pattison, P., & Robins, G. (2006). A spatial model for social networks. Physica A: Statistical Mechanics and its Applications, 360 (1), 99–120.Google Scholar
Zachary, W. W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33 (4), 452–473.CrossRefGoogle Scholar