## Assortativity and clustering of sparse random intersection graphs.(English)Zbl 1278.05223

Summary: We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of adjacent nodes (called the assortativity coefficient), the expected number of common neighbours of adjacent nodes, and the expected degree of a neighbour of a node of a given degree $$k$$. These expressions are written in terms of the asymptotic degree distribution and, alternatively, in terms of the parameters defining the underlying random graph model.

### MSC:

 05C80 Random graphs (graph-theoretic aspects) 05C82 Small world graphs, complex networks (graph-theoretic aspects) 05C42 Density (toughness, etc.) 91D30 Social networks; opinion dynamics
Full Text: