  Random intersection graphs have received much interest and been used in
diverse applications. They are naturally induced in modeling secure sensor
networks under random key predistribution schemes, as well as in modeling the
topologies of social networks including common-interest networks, collaboration
networks, and actor networks. Simply put, a random intersection graph is
constructed by assigning each node a set of items in some random manner and
then putting an edge between any two nodes that share a certain number of
items.
  Broadly speaking, our work is about analyzing random intersection graphs, and
models generated by composing it with other random graph models including
random geometric graphs and Erd\H{o}s-R\'enyi graphs. These compositional
models are introduced to capture the characteristics of various complex natural
or man-made networks more accurately than the existing models in the
literature. For random intersection graphs and their compositions with other
random graphs, we study properties such as ($k$-)connectivity,
($k$-)robustness, and containment of perfect matchings and Hamilton cycles. Our
results are typically given in the form of asymptotically exact probabilities
or zero-one laws specifying critical scalings, and provide key insights into
the design and analysis of various real-world networks.
