Poisson approximation of induced subgraph counts in an inhomogeneous random intersection graph model
Bull. Korean Math. Soc. 2019 Vol. 56, No. 5, 1199-1210
https://doi.org/10.4134/BKMS.b180971
Published online September 30, 2019
Yilun Shang
Northumbria University
Abstract : 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
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