相关论文: The connected component of the partial duplication…

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…

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…

Recently, van der Hofstad, Komj\'{a}thy, and Vadon (2022) identified the critical point for the emergence of a giant connected component for the bipartite configuration model (BCM) and used this to analyze its associated random intersection…

We study an evolving spatial network in which sequentially arriving vertices are joined to existing vertices at random according to a rule that combines preference according to degree with preference according to spatial proximity. We…

We study the largest component of a random (multi)graph on n vertices with a given degree sequence. We let n tend to infinity. Then, under some regularity conditions on the degree sequences, we give conditions on the asymptotic shape of the…

Consider a subcritical branching Markov chain. Let $Z_n$ denote the counting measure of particles of generation $n$. Under some conditions, we give a probabilistic proof for the existence of the Yaglom limit of $(Z_n)_{n\in\mathbb{N}}$ by…

We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…

In this paper, we study a bipartite analogue of the `random graphs evolving by degrees' process. We are given a bipartitioned set of vertices $V$ into two disjoint parts ${L}$ and ${R}$ and possibly unequal positive constants $\alpha$ and…

Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…

Benjamini and Schramm introduced the notion of distributional limit of a sequence of graphs with uniformly bounded valence and studied such limits in the case that the involved graphs are planar. We investigate distributional limits of…

We study Turing bifurcations on one-dimensional random ring networks where the probability of a connection between two nodes depends on the distance between the two nodes. Our approach uses the theory of graphons to approximate the graph…

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…

For irreducible, time-homogeneous Markov networks, mutual linearity has recently been established for both occupation probabilities and network currents in the stationary regime as well as in the non-stationary regime in Laplace space. The…

In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on $n$ vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in $n$ in case of {\em semi-regular} degree…

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…

Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that…

Exchangeable random graphs, which include some of the most widely studied network models, have emerged as the mainstay of statistical network analysis in recent years. Graphons, which are the central objects in graph limit theory, provide a…

We consider the component structure of a recent model of random graphs on the hyperbolic plane that was introduced by Krioukov et al. The model exhibits a power law degree sequence, small distances and clustering, features that are…