Component Evolution in General Random Intersection Graphs

Abstract

Random intersection graphs (RIGs) are an important random structure with applications in social networks, epidemic networks, blog readership, and wireless sensor networks. RIGs can be interpreted as a model for large randomly formed non-metric data sets. We analyze the component evolution in general RIGs, and give conditions on existence and uniqueness of the giant component. Our techniques generalize existing methods for analysis of component evolution: we analyze survival and extinction properties of a dependent, inhomogeneous Galton-Watson branching process on general RIGs. Our analysis relies on bounding the branching processes and inherits the fundamental concepts of the study of component evolution in Erdős-Rényi graphs. The major challenge comes from the underlying structure of RIGs, which involves its both the set of nodes and the set of attributes, as well as the set of different probabilities among the nodes and attributes.

References in corpus (2)

• Why social networks are different from other types of networks
• Bipartite Graphs as Models of Complex Networks

Cited by in corpus (9)

• Connectivity in Secure Wireless Sensor Networks under Transmission Constraints
• On the strengths of connectivity and robustness in general random intersection graphs
• On Connectivity and Robustness in Random Intersection Graphs
• On Topological Properties of Wireless Sensor Networks under the q-Composite Key Predistribution Scheme with On/Off Channels
• On $k$-connectivity and minimum vertex degree in random $s$-intersection graphs
• Random intersection graphs and their applications in security, wireless communication, and social networks
• Clustering function: a measure of social influence
• Analyzing resilience of interest-based social networks against node and link failures
• On connectivity in a general random intersection graph