Diameter, connectivity, and phase transition of the uniform random intersection graph
نویسندگان
چکیده
منابع مشابه
Connectivity of the uniform random intersection graph
A uniform random intersection graph G(n,m, k) is a random graph constructed as follows. Label each of n nodes by a randomly chosen set of k distinct colours taken from some finite set of possible colours of size m. Nodes are joined by an edge if and only if some colour appears in both their labels. These graphs arise in the study of the security of wireless sensor networks, in particular when m...
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Non-uniform hypergraphs appear in various domains of computer science as in the satisfiability problems and in data analysis. We analyse a general model where the probability for an edge of size t to belong to the hypergraph depends of a parameter ωt of the model. It is a natural generalization of the models of graphs used by Flajolet, Knuth and Pittel [1] and Janson, Knuth, Luczak and Pittel [...
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Abstract There has been growing interest in studies of general random intersection graphs. In this paper, we consider a general random intersection graphG(n,−→a ,−→ Kn, Pn) defined on a set Vn comprising n vertices, where−→a is a probability vector (a1, a2, . . . , am) and −→ Kn is (K1,n,K2,n, . . . ,Km,n). This graph has been studied in the literature [10,11,20,29] including a most recent work...
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We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase transition. We give bounds on the size of the largest components before and after this transition. We also prove that the largest component after the transiti...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2011
ISSN: 0012-365X
DOI: 10.1016/j.disc.2011.05.029