Institute for Cyber Security, The University of Texas at San Antonio, San Antonio, TX 78249, USA
Copyright © 2011 Yilun Shang. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study isolated vertices and connectivity in the random intersection graph . A Poisson convergence for the number of isolated vertices is
determined at the threshold for absence of isolated vertices, which is equivalent to
the threshold for connectivity. When and , we give the asymptotic
probability of connectivity at the threshold for connectivity. Analogous results are
well known in Erdős-Rényi random graphs.