Related papers: Directed random graphs with given degree distribut…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…
We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier…
Many complex systems show non-pairwise interactions, which can be captured by hypergraphs. In this work, we propose an edge-swapping method to sample random directed hypergraphs with fixed vertex and hyperarc degrees, which can be applied…
Let $G$ be a large (simple, unlabeled) dense graph on $n$ vertices. Suppose that we only know, or can estimate, the empirical distribution of the number of subgraphs $F$ that each vertex in $G$ participates in, for some fixed small graph…
We consider a stochastic directed graph on the integers whereby a directed edge between $i$ and a larger integer $j$ exists with probability $p_{j-i}$ depending solely on the distance between the two integers. Under broad conditions, we…
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…
For a given permutation $\pi_n$ in $S_n$, a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (\pi_n(i) - \pi_n (j)) < 0$. In this paper, we study various statistics of random…
We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…
In this paper, we study the connectivity of a one-dimensional soft random geometric graph (RGG). The graph is generated by placing points at random on a bounded line segment and connecting pairs of points with a probability that depends on…
Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…
In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
A random geometric digraph $G_n$ is constructed by taking $\{X_1,X_2,... X_n\}$ in $\mathbb{R}^2$ independently at random with a common bounded density function. Each vertex $X_i$ is assigned at random a sector $S_i$ of central angle…
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
We prove that for each $k\ge0$, the probability that a root vertex in a random planar graph has degree $k$ tends to a computable constant $d_k$, so that the expected number of vertices of degree $k$ is asymptotically $d_k n$, and moreover…
Random networks are intensively used as null models to investigate properties of complex networks. We describe an efficient and accurate algorithm to generate arbitrarily two-point correlated undirected random networks without self- or…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…