Related papers: Horizontal visibility graph of a random restricted…
Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…
For a random graph on n vertices where the edges appear with individual rates, we give exact formulas for the expected time at which the number of components has gone down to k and the expected length of the corresponding minimal spanning…
We study the random graph G_{n,\lambda/n} conditioned on the event that all vertex degrees lie in some given subset S of the non-negative integers. Subject to a certain hypothesis on S, the empirical distribution of the vertex degrees is…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
We describe the asymptotic behaviour of large degrees in random hyperbolic graphs, for all values of the curvature parameter $ \alpha$. We prove that, with high probability, the node degrees satisfy the following ordering property: the…
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…
We study the susceptibility, i.e., the mean cluster size, in random graphs with given vertex degrees. We show, under weak assumptions, that the susceptibility converges to the expected cluster size in the corresponding branching process. In…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic…
Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random…
We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in…
Random $s$-intersection graphs have recently received considerable attention in a wide range of application areas. In such a graph, each vertex is equipped with a set of items in some random manner, and any two vertices establish an…
Highly-regular graphs can be regarded as a combinatorial generalization of distance-regular graphs. From this standpoint, we study combinatorial aspects of highly-regular graphs. As a result, we give the following three main results in this…
We study the number of isolated nodes in a soft random geometric graph whose vertices constitute a Poisson process on the torus of length L (the line segment [0,L] with periodic boundary conditions), and where an edge is present between two…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…
Due to the fact that the numbers of annually published papers have witnessed a linear growth in some citation networks, a geometric model is thus proposed to predict some statistical features of those networks, in which the academic…
We consider the probability that a spanning tree chosen uniformly at random from a graph can be partitioned into a fixed number $k$ of trees of equal size by removing $k-1$ edges. In that case, the spanning tree is called {\em splittable}.…
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. This confirms a conjecture made in 1997. As a result, many interesting functions of…