相关论文: Properties of stochastic Kronecker graphs

In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…

Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…

We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) $k$ are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a…

We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…

In this article, we study random graphs with a given degree sequence $d_1, d_2, \cdots, d_n$ from the configuration model. We show that under mild assumptions of the degree sequence, the spectral distribution of the normalized Laplacian…

Bi-partite ribbon graphs arise in organising the large $N$ expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is an algebra $\mathcal{K}(n)$, with basis given by bi-partite…

We study the asymptotic shape of random unlabelled graphs subject to certain subcriticality conditions. The graphs are sampled with probability proportional to a product of Boltzmann weights assigned to their $2$-connected components. As…

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model…

In this paper we consider a simple model of random graph process with {\it hard} copying as follows: At each time step $t$, with probability $0<\alpha\leq 1$ a new vertex $v_t$ is added and $m$ edges incident with $v_t$ are added in the…

We provide precise asymptotic estimates for the number of several classes of labelled cubic planar graphs, and we analyze properties of such random graphs under the uniform distribution. This model was first analyzed by Bodirsky et al.…

We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…

A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full…

Recently, real world networks having constant/shrinking diameter along with power-law degree distribution are observed and investigated in literature. Taking an inspiration from these findings, we propose a deterministic complex network…

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…

A covariance graph is an undirected graph associated with a multivariate probability distribution of a given random vector where each vertex represents each of the different components of the random vector and where the absence of an edge…

This paper explores various distributional aspects of random variables defined as the ratio of two independent positive random variables where one variable has an $\alpha$-stable law, for $0<\alpha<1$, and the other variable has the law…

We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…

Bilateral agreement based random undirected graphs were introduced and analyzed by La and Kabkab in 2015. The construction of the graph with $n$ vertices in this model uses a (random) preference order on other $n-1$ vertices and each vertex…

Random key graphs are random graphs induced by the random key predistribution scheme of Eschenauer and Gligor under the assumption of full visibility. For this class of random graphs we show the existence of a zero-one law for the…