Related papers: Assortativity and bidegree distributions on Bernou…
We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…
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…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
We investigate the degree distribution resulting from graph generation models based on rank-based attachment. In rank-based attachment, all vertices are ranked according to a ranking scheme. The link probability of a given vertex is…
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY)…
We develop an approach to generate random graphs to a target level of assortativity by using copula structures in graphons. Unlike existing random graph generators, we do not use rewiring or binning approaches to generate the desired random…
Given a graphical degree sequence ${\bf d}=(d_1,\ldots, d_n)$, let $G(n, {\bf d})$ denote a uniformly random graph on vertex set $[n]$ where vertex $ i$ has degree $d_i$ for every $1\le i\le n$. We give upper and lower bounds on the joint…
The on-line nearest-neighbour graph on a sequence of $n$ uniform random points in $(0,1)^d$ ($d \in \N$) joins each point after the first to its nearest neighbour amongst its predecessors. For the total power-weighted edge-length of this…
The availability of large scale streaming network data has reinforced the ubiquity of power-law distributions in observations and enabled precision measurements of the distribution parameters. The increased accuracy of these measurements…
It is challenging for generative models to learn a distribution over graphs because of the lack of permutation invariance: nodes may be ordered arbitrarily across graphs, and standard graph alignment is combinatorial and notoriously…
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…
In search of many social and economical systems, it is found that node strength distribution as well as degree distribution demonstrate the behavior of power-law with droop-head and heavy-tail. We present a new model for the growth of…
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…
Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$ left vertices, n right vertices, t edges, and each vertex of degree at least one. We…
Degree ssortativity is the tendency for nodes of high degree (resp.low degree) in a graph to be connected to high degree nodes (resp. to low degree ones). It is sually quantified by the Pearson correlation coefficient of the degree-degree…
We propose a simple random process inducing various types of random graphs and the scale free random graphs among others. The model is of a threshold nature and differs from the preferential attachment approach discussed in the literature…
We study a generalisation of the random recursive tree (RRT) model and its multigraph counterpart, the uniform directed acyclic graph (DAG). Here, vertices are equipped with a random vertex-weight representing initial inhomogeneities in the…
We investigate a growing network model that combines preferential and uniform attachment with two distinct mechanisms of edge deletion. In addition to the usual uniform probability edge deletion, we introduce a novel node-based rule in…
Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…
We present a comprehensive extension of the latent position network model known as the random dot product graph to accommodate multiple graphs -- both undirected and directed -- which share a common subset of nodes, and propose a method for…