We consider a family of random graphs with a given expected degree sequence. Each edge
is chosen independently with probability proportional to the product of the expected degrees …

We consider the random graph model G(w) for a given expected degree sequence
\mathbfw=(w_1,w_2,...,w_n). If the expected average degree is strictly greater than 1, then …

Given a sequence of nonnegative real numbers λ0, λ1,… that sum to 1, we consider a
random graph having approximately λin vertices of degree i. In [12] the authors essentially …

Random intersection graphs are a model of random graphs in which each vertex is assigned
a subset of a set of objects independently and two vertices are adjacent if their assigned …

We study the largest component of a random (multi) graph on n vertices with a given degree
sequence. We let n→∞. Then, under some regularity conditions on the degree sequences …

Limiting distributions are derived for the sparse connected components that are present
when a random graph on n vertices has approximately 1/2n edges. In particular, we show …

According to a fundamental result of Erdös and Rényi, the structure of a random graph
${G_M} $ changes suddenly when $ M\sim n/2$: if $ M=\left\lfloor {cn}\right\rfloor $ and …

Given a sequence of nonnegative real numbers λ0, λ1… which sum to 1, we consider
random graphs having approximately λi n vertices of degree i. Essentially, we show that if Σ i …

The paper sets out to investigate the degree sequences d 1⩾ d 2⩾…⩾ dn of random graphs
of order n in which the edges are chosen independently and with the same probability p, 0< …

Abstract Let e1, e′ 1; e2, e′ 2;…; ei, e′ i;⋅⋅⋅ be a sequence of ordered pairs of edges
chosen uniformly at random from the edge set of the complete graph Kn (ie we sample with …