Component evolution in general random intersection graphs
- Los Alamos National Laboratory
- CLAREMONT GRADUATE UNIV.
We analyze component evolution in general random intersection graphs (RIGs) and give conditions on existence and uniqueness of the giant component. Our techniques generalize the existing methods for analysis on component evolution in RIGs. That is, 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 from the study on component evolution in Erdos-Renyi graphs. The main challenge becomes from the underlying structure of RIGs, when the number of offsprings follows a binomial distribution with a different number of nodes and different rate at each step during the evolution. RIGs can be interpreted as a model for large randomly formed non-metric data sets. Besides the mathematical analysis on component evolution, which we provide in this work, we perceive RIGs as an important random structure which has already found applications in social networks, epidemic networks, blog readership, or wireless sensor networks.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 993122
- Report Number(s):
- LA-UR-10-01561; LA-UR-10-1561; TRN: US201023%%204
- Resource Relation:
- Journal Volume: 6516; Conference: AOFA 10 ; June 25, 2010 ; Vienna, Austria
- Country of Publication:
- United States
- Language:
- English
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