Abstract
Google+ (G+ in short) is a directed online social network where nodes have either reciprocal (bidirectional) edges or parasocial (one-way) edges. As reciprocal edges represent strong social ties, we study the core structure of the subgraph formed by them, referred to as the reciprocal network of G+. We develop an effective three-step procedure to hierarchically extract and unfold the core structure of this reciprocal network. This procedure builds up and generalizes ideas from the existing k-shell decomposition and clique percolation approaches, and produces higher-level representations of the core structure of the G+ reciprocal network. Our analysis shows that there are seven subgraphs (“communities”) comprising of dense clusters of cliques lying at the center of the core structure of the G+ reciprocal network, through which other communities of cliques are richly connected. Together they form the core to which “peripheral” sparse subgraphs are attached.
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Notes
- 1.
In this paper we use the terms “user" and “node" interchangeable.
- 2.
It contains more than 90 % of the nodes with at least one reciprocal edge in G+. Hence, our analysis of the dataset is eventually approximate.
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Acknowledgments
This research was supported in part by DoD ARO MURI Award W911NF-12-1-0385, DTRA grant HDTRA1- 14-1-0040 and NSF grant CNS-1411636. We thank the authors of [6] for the datasets.
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Dumba, B., Zhang, ZL. (2016). Unfolding the Core Structure of the Reciprocal Graph of a Massive Online Social Network. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_58
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