Abstract
We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) k are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a collection of attributes and two vertices are adjacent whenever they share a common attribute. We show that the probability obeys the scaling \(k^{-\delta }\) as \(k\rightarrow +\infty \). Our results are mathematically rigorous. The parameter \(0\le \delta \le 1\) is determined by the tail indices of power law random weights defining the links between vertices and attributes.
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Bloznelis, M., Petuchovas, J. (2017). Correlation Between Clustering and Degree in Affiliation Networks. In: Bonato, A., Chung Graham, F., Prałat, P. (eds) Algorithms and Models for the Web Graph. WAW 2017. Lecture Notes in Computer Science(), vol 10519. Springer, Cham. https://doi.org/10.1007/978-3-319-67810-8_7
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DOI: https://doi.org/10.1007/978-3-319-67810-8_7
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