Bulletin of the
Korean Mathematical Society BKMS

In this paper, we consider a class of inhomogeneous random intersection graphs by assigning random weight to each vertex and two vertices are adjacent if they choose some common elements. In the inhomogeneous random intersection graph model, vertices with larger weights are more likely to acquire many elements. We show the Poisson convergence of the number of induced copies of a fixed subgraph as the number of vertices $n$ and the number of elements $m$, scaling as $m=\lfloor\beta n^{\alpha}\rfloor$ $(\alpha,\beta>0)$, tend to infinity.

Keywords: random graph, intersection graph, Poisson approximation, Stein's method, subgraph count

MSC numbers: Primary 60F05, 05C80, 62E17