An (α,β)-community is a subset of vertices C with each vertex in C connected to at least β vertices of C (self-loops counted) and each vertex outside of C connected to at most α vertices of C (α < β) . In this paper, we present a heuristic (α,β)-Community algorithm, which in practice successfully finds (α,β)-communities of a given size. The structure of (α,β)-communities in several large-scale social graphs is explored, and a surprising core structure is discovered by taking the intersection of a group of massively overlapping (α,β)-communities. For large community size k, the (α,β)-communities are well clustered into a small number of disjoint cores, and there are no isolated (α,β)-communities scattered between these densely-clustered cores. The (α,β)-communities from the same group have significant overlap among them, and those from distinct groups have extremely small pairwise resemblance. The number of cores decreases as k increases, and there are no bridges of intermediate (α,β)-communities connecting one core to another. The cores obtained for a smaller k either disappear or merge into the cores obtained for a larger k. Further, similar experiments on random graph models demonstrate that the core structure displayed in various social graphs is due to the underlying social structure of these real-world networks, rather than due to high-degree vertices or a particular degree distribution.
- Social Network
- Random Graph
- Degree Distribution
- Maximal Clique
- Social Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Authors are listed alphabetically.
This research was partially supported by the U.S. Air Force Office of Scientific Research under Grant FA9550-09-1-0675, the National Natural Science Foundation of China under Grant 60553001, and the National Basic Research Program of China under Grant 2007CB807900 and 2007CB807901.
This is a preview of subscription content, access via your institution.
Tax calculation will be finalised at checkout
Purchases are for personal use onlyLearn about institutional subscriptions
Unable to display preview. Download preview PDF.
Choudhury, M.D., Lin, Y.-R., Sundaram, H., Candan, K., Xie, L., Kelliher, A.: How does the sampling strategy impact the discovery of information diffusion in social media? In: Proc. 4th Int’l AAAI Conf. Weblogs and Social Media, ICWSM (2010)
Choudhury, M.D., Sundaram, H., John, A., Seligmann, D.D., Kelliher, A.: Birds of a feather: does attribute homophily impact information diffusion on social media? (under review)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70, 06111 (2004)
Gaertler, M.: Clustering. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. LNCS, vol. 3418, pp. 178–215. Springer, Heidelberg (2005)
Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. USA 99(12), 7821–7826 (2002)
He, J., Hopcroft, J.E., Liang, H., Supasorn, S., Wang, L.: Detecting the structure of social networks using (α, β)-communities. Tech. rep., Cornell University (2011), http://hdl.handle.net/1813/22415
Lang, K., Rao, S.: A flow-based method for improving the expansion or conductance of graph cuts. In: Bienstock, D., Nemhauser, G.L. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 325–337. Springer, Heidelberg (2004)
Leskovec, J., Lang, K., Dasgupta, A., Mahoney, M.: Statistical properties of community structure in large social and information networks. In: Proc. 18th Int’l World Wide Web Conf. WWW (2008)
Mishra, N., Schreiber, R., Stanton, I., Tarjan, R.E.: Finding strongly-knit clusters in social networks. Internet Mathematics 5(1-2), 155–174 (2009)
Newman, M.E.J.: Detecting community structure in networks. The European Physical J. B 38, 321–330 (2004)
Newman, M.E.J.: Fast algorithm for detecting community structure in networks. Phys. Rev. E 69, 066133 (2004)
Newman, M.E.J.: Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 036104 (2006)
Newman, M.E.J.: Modularity and community structure in networks. Proc. Natl. Acad. Sci. USA 103(23), 8577–8582 (2006)
Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69, 026113 (2004)
Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)
Editors and Affiliations
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
He, J., Hopcroft, J., Liang, H., Suwajanakorn, S., Wang, L. (2011). Detecting the Structure of Social Networks Using (α,β)-Communities. In: Frieze, A., Horn, P., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2011. Lecture Notes in Computer Science, vol 6732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21286-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21285-7
Online ISBN: 978-3-642-21286-4