Related papers: Degree distribution of an inhomogeneous random int…
We establish the asymptotic degree distribution of the typical vertex of inhomogeneous and passive random intersection graphs under the minimal moment conditions.
The bivariate distribution of degrees of adjacent vertices (degree-degree distribution) is an important network characteristic defining the statistical dependencies between degrees of adjacent vertices. We show the asymptotic degree-degree…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132]. For…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
We study a variant of the standard random intersection graph model ($G(n,m,F,H)$) in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the distributions of these weights, the…
In several scale free graph models the asymptotic degree distribution and the characteristic exponent change when only a smaller set of vertices is considered. Looking at the common properties of these models, we present sufficient…
Let $X_1,X_2,...$ be an infinite sequence of i.i.d. random vectors distributed exponentially with parameter $\lam .$ For each $y$ and $n\geq 1,$ form a graph $G_n(y)$ with vertex set $V_n = \{X_1,...,X_n\},$ two vertices are connected if…
In this paper, we derive the asymptotic distribution of the number of copies of a fixed graph $H$ in a random graph $G_n$ sampled from a sparse graphon model. Specifically, we provide a refined analysis that separates the contributions of…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
In the sufficiently sparse case, we find the probability that a uniformly random bipartite graph with given degree sequence contains no edge from a specified set of edges. This enables us to enumerate loop-free digraphs and oriented graphs…
We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
We provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…
We consider an inhomogeneous Erd\H{o}s-R\'enyi random graph ensemble with exponentially decaying random disconnection probabilities determined by an i.i.d. field of variables with heavy tails and infinite mean associated to the vertices of…
For a random intersection graph with a power law degree sequence having a finite mean and an infinite variance we show that the global clustering coefficient admits a tunable asymptotic distribution.
We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…