Degree Distributions in General Random Intersection Graphs
نویسنده
چکیده
Random intersection graphs, denoted by G(n,m, p), are introduced in [9, 14] as opposed to classical Erdős-Rényi random graphs. Let us consider a set V with n vertices and another universal set W with m elements. Define a bipartite graph B(n,m, p) with independent vertex sets V and W . Edges between v ∈ V and w ∈ W exist independently with probability p. The random intersection graph G(n,m, p) derived from B(n,m, p) is defined on the vertex set V with vertices v1, v2 ∈ V adjacent if and only if there exists some w ∈ W such that both v1 and v2 are adjacent to w in B(n,m, p). To get an interesting graph structure and bounded average degree, the work [15] sets m = ⌊n⌋ and p = cn for some α, c > 0 and determines the distribution of the degree of a typical vertex. Some related properties for this model are recently investigated; for example, independent sets [11] and component evolution [1, 10]. A generalized random intersection graph is introduced in [5] by allowing a more general connection probability in the underlying bipartite graph. The corresponding vertex degrees are also studied by some authors, see e.g. [2, 7, 8], and shown to be asymptotically Poisson distributed. In this paper, we consider a variant model of random intersection graphs, where each vertex and element are associated with a random weight, in order to obtain a larger class of degree distributions. Our model, referred to as G(n,m, F,H), is defined as follows.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 17 شماره
صفحات -
تاریخ انتشار 2010