相关论文: Expectation and Variance of the Degree of a Node i…

We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…

We study a variant of the standard random intersection graph model ($G(n,m,F,H)$) in which random weights are assigned to both vertex types in the bipartite structure. Under certain assumptions on the distributions of these weights, the…

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight…

In this article, we explicitly derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights. We determine the asymptotics of the degree distribution for large…

The network topology can be described by the number of nodes and the interconnections among them. The degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability…

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,…

We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be…

A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…

We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…

We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…

We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

Node betweenness has been studied recently by a number of authors, but until now less attention has been paid to edge betweenness. In this paper, we present an exact analytic study of edge betweenness in evolving scale-free and…

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…

We give an asymptotic expression for the expected number of spanning trees in a random graph with a given degree sequence $\boldsymbol{d}=(d_1,\ldots, d_n)$, provided that the number of edges is at least $n + \textstyle{\frac{1}{2}}…

The focus of this work is on estimation of the in-degree distribution in directed networks from sampling network nodes or edges. A number of sampling schemes are considered, including random sampling with and without replacement, and…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

A rooted arborescence of a directed graph is a spanning tree directed towards a particular vertex. A recent work of Chepuri et al. showed that the arborescences of a covering graph of a directed graph G are closely related to the…

We study the height of a spanning tree $T$ of a graph $G$ obtained by starting with a single vertex of $G$ and repeatedly selecting, uniformly at random, an edge of $G$ with exactly one endpoint in $T$ and adding this edge to $T$.

The weighted spanning tree enumerator of a graph $G$ with weighted edges is the sum of the products of edge weights over all the spanning trees in $G$. In the special case that all of the edge weights equal $1$, the weighted spanning tree…