Title: Correlation between clustering and degree in affiliation networks,
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 $k\to+\infty$. 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.