相关论文: Connection probability for random graphs with give…
We demonstrate how to generalize two of the most well-known random graph models, the classic random graph, and random graphs with a given degree distribution, by the introduction of hidden variables in the form of extra degrees of freedom,…
We introduce a measure of {\em greedy connectivity} for geographical networks (graphs embedded in space) and where the search for connecting paths relies only on local information, such as a node's location and that of its neighbors.…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
In this paper, we study the connectivity in one-dimensional ad hoc wireless networks with an fixed access point. In recent years, various closed expressions for the probability of connectivity on one-dimensional networks (interval graphs)…
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…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
We find conditions for the connectivity of inhomogeneous random graphs with intermediate density. Our results generalize the classical result for G(n, p), when p = c log n/n. We draw n independent points X_i from a general distribution on a…
The configuration model is the most natural model to generate a random multigraph with a given degree sequence. We use the notion of dense graph limits to characterize the special form of limit objects of convergent sequences of…
Research in transportation frequently involve modelling and predicting attributes of events that occur at regular intervals. The event could be arrival of a bus at a bus stop, the volume of a traffic at a particular point, the demand at a…
Random increasing k-trees represent an interesting, useful class of strongly dependent graphs for which analytic-combinatorial tools can be successfully applied. We study in this paper a notion called connectivity-profile and derive…
This paper provides time-dependent expressions for the expected degree distribution of a given network that is subject to growth, as a function of time. We consider both uniform attachment, where incoming nodes form links to existing nodes…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
We consider the preferential attachment model. This is a growing random graph such that at each step a new vertex is added and forms $m$ connections. The neighbors of the new vertex are chosen at random with probability proportional to…
Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we…