Correlation between clustering and degree in affiliation networks

2018/01/04 by Bloznelis, Mindaugas, Petuchovas, Justinas
#05C80 #05C82 #90B15 #91D30 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI)

paper · doi:10.48550/arxiv.1801.01521

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^-δ as k→+∞. 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.

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