Abstract
The purpose of this article is to link high density in social networks with their underlying bipartite affiliation structure. Density is represented by an average number of a node’s neighbors (i.e. node degree or node rank). It is calculated by dividing a number of edges in a graph by a number of vertices. We compare an average node degree in real-life affiliation networks to an average node degree in social networks obtained by projecting an affiliation network onto a user modality. We have found recently that the asymptotic Newmann’s explicit formula relating node degree distributions in an affiliation network to the density of a projected graph overestimates the latter value for real-life datasets. We have also observed that this property can be attributed to the local tree-like structure assumption. In this article we propose a procedure to estimate the density of a projected graph by means of a mixture of an exponential and a power-law distributions. We show that our method gives better density estimates than the classic formula.
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Chojnacki, S., Ciesielski, K., Kłopotek, M. (2010). Node Degree Distribution in Affiliation Graphs for Social Network Density Modeling. In: Bolc, L., Makowski, M., Wierzbicki, A. (eds) Social Informatics. SocInfo 2010. Lecture Notes in Computer Science, vol 6430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16567-2_4
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DOI: https://doi.org/10.1007/978-3-642-16567-2_4
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