  Random intersection graphs have received much attention for nearly two
decades, and currently have a wide range of applications ranging from key
predistribution in wireless sensor networks to modeling social networks. In
this paper, we investigate the strengths of connectivity and robustness in a
general random intersection graph model. Specifically, we establish sharp
asymptotic zero-one laws for $k$-connectivity and $k$-robustness, as well as
the asymptotically exact probability of $k$-connectivity, for any positive
integer $k$. The $k$-connectivity property quantifies how resilient is the
connectivity of a graph against node or edge failures. On the other hand,
$k$-robustness measures the effectiveness of local diffusion strategies (that
do not use global graph topology information) in spreading information over the
graph in the presence of misbehaving nodes. In addition to presenting the
results under the general random intersection graph model, we consider two
special cases of the general model, a binomial random intersection graph and a
uniform random intersection graph, which both have numerous applications as
well. For these two specialized graphs, our results on asymptotically exact
probabilities of $k$-connectivity and asymptotic zero-one laws for
$k$-robustness are also novel in the literature.
