Related papers: Degree distribution of an inhomogeneous random int…

We study the properties of the giant connected component in random graphs with arbitrary degree distribution. We concentrate on the degree-degree correlations. We show that the adjoining nodes in the giant connected component are correlated…

We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function $nf(\cdot)$, where $n\in \mathbb{N}$, and $f$ is a probability density…

We study graphs whose vertex degree tends and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth.…

We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and random set partitions of size $n.$ Our main results are formulas expressing the expected degree of graph nodes in…

Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs,…

Let S and T be vectors of positive integers with the same sum. We study the uniform distribution on the space of simple bipartite graphs with degree sequence S in one part and T in the other; equivalently, binary matrices with row sums S…

How can we approximate sparse graphs and sequences of sparse graphs (with unbounded average degree)? We consider convergence in the first $k$ moments of the graph spectrum (equivalent to the numbers of closed $k$-walks) appropriately…

We consider random geometric graphs on the plane characterized by a non-uniform density of vertices. In particular, we introduce a graph model where $n$ vertices are independently distributed in the unit disc with positions, in polar…

For a finite random graph, we defined a simple model of statistical mechanics. We obtain an annealed asymptotic result for the random partition function for this model on finite random graphs as n; the size of the graph is very large. To…

Using an associated branching process as the basis of our approximation, we show that typical inter-point distances in a multitype random intersection graph have a defective distribution, which is well described by a mixture of translated…

Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce goodness-of-fit tests for two classes of models.…

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…

Let $G$ be a finite, simple, and undirected graph of order $n$ and average degree $d$. Up to terms of smaller order, we characterize the minimal intervals $I$ containing $d$ that are guaranteed to contain some vertex degree. In particular,…

We show that if a graph contains few induced copies of a given graph then its edges are distribited unevenly.

We study the critical behavior of inhomogeneous random graphs where edges are present independently but with unequal edge occupation probabilities. The edge probabilities are moderated by vertex weights, and are such that the degree of…

We count the asymptotic number of triangles in uniform random graphs where the degree distribution follows a power law with degree exponent $\tau\in(2,3)$. We also analyze the local clustering coefficient $c(k)$, the probability that two…

In this paper we study the degree sequence of the permutation graph $G_{\pi_n}$ associated with a sequence $\pi_n\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and…

We consider first passage percolation on sparse random graphs with prescribed degree distributions and general independent and identically distributed edge weights assumed to have a density. Assuming that the degree distribution satisfies a…

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…