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

Random intersection graphs and their applications in security, wireless communication, and social networks