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 (Formula Presented). Our results are mathematically rigorous. The parameter 0 ≤ δ ≤ 1 is determined by the tail indices of power law random weights defining the links between vertices and attributes.
CITATION STYLE
Bloznelis, M., & Petuchovas, J. (2017). Correlation between clustering and degree in affiliation networks. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10519 LNCS, 90–104. https://doi.org/10.1007/978-3-319-67810-8_7
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