Detecting the Structure of Social Networks Using (α,β)-Communities
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.
Unable to display preview. Download preview PDF.
- 1.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)Google Scholar
- 2.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)Google Scholar
- 3.Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Phys. Rev. E 70, 06111 (2004)Google Scholar
- 6.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
- 8.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)Google Scholar