Abstract
We study here the clustering of directed social graphs. The clustering coefficient has been introduced to capture the social phenomena that a friend of a friend tends to be my friend. This metric has been widely studied and has shown to be of great interest to describe the characteristics of a social graph. In fact, the clustering coefficient is adapted for a graph in which the links are undirected, such as friendship links (Facebook) or professional links (LinkedIn). For a graph in which links are directed from a source of information to a consumer of information, it is no longer adequate. We show that former studies have missed much of the information contained in the directed part of such graphs. We thus introduce a new metric to measure the clustering of a directed social graph with interest links, namely the interest clustering coefficient. We compute it (exactly and using sampling methods) on a very large social graph, a Twitter snapshot with 505 million users and 23 billion links. We additionally provide the values of the formerly introduced directed and undirected metrics, a first on such a large snapshot. We exhibit that the interest clustering coefficient is larger than classic directed clustering coefficients introduced in the literature. This shows the relevancy of the metric to capture the informational aspects of directed graphs.
This work has been supported by the French government through the UCA JEDI (ANR-15-IDEX-01), EUR DS4H (ANR-17-EURE-004) Investments in the Future projects, and ANR DIGRAPHS, by the SNIF project, and by Inria associated team EfDyNet. The authors are grateful to the OPAL infrastructure from Université Côte d’Azur for providing resources and support.
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Trolliet, T., Cohen, N., Giroire, F., Hogie, L., Pérennes, S. (2021). Interest Clustering Coefficient: A New Metric for Directed Networks Like Twitter. In: Benito, R.M., Cherifi, C., Cherifi, H., Moro, E., Rocha, L.M., Sales-Pardo, M. (eds) Complex Networks & Their Applications IX. COMPLEX NETWORKS 2020 2020. Studies in Computational Intelligence, vol 944. Springer, Cham. https://doi.org/10.1007/978-3-030-65351-4_48
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DOI: https://doi.org/10.1007/978-3-030-65351-4_48
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