Equivalence of a random intersection graph and G (n ,p )

In the random graph G(n, P), . . .

Random intersection graphs when m=omega(n): An equivalence theorem relating the evolution of the G(n, m, p) and G(n, p) models

When the random intersection graph G(n,m, p) proposed by Karoński, Scheinerman, and Singer-Cohen in [8] is compared with the independent-edge G(n, p), the evolutions are different under some values of m and equivalent under others. In particular, when m = nα and α > 6, the total variation distance between the graph random variables has limit 0.

Random Intersection Graph Process

Vertices of an affiliation network are linked to features and two vertices are declared adjacent whenever they share a common feature. We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks. We establish the asymptotic degree distribution and provide explicit asymptotic formulas for assortativity and clustering coefficients showing how these edge...

THE (△,□)-EDGE GRAPH G△,□ OF A GRAPH G

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

Planarity of Intersection Graph of submodules of a Module

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...