Related papers: Cumulant method for weighted random connection mod…
Letting $\mathcal{M}$ denote the space of finite measures on $\mathbb{N}$, and $\mu_\lambda\in\mathcal{M}$ denote the Poisson distribution with parameter $\lambda$, the function $W:[0,1]^2\to\mathcal{M}$ given by \[ W(x,y)=\mu_{c\log x\log…
We consider a class of simple, non-trivial models of evolving weighted scale-free networks. The network evolution in these models is determined by attachment of new vertices to ends of preferentially chosen weighted edges. Resulting…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
Joining records with all other records that meet a linkage condition can result in an astronomically large number of combinations due to many-to-many relationships. For such challenging (acyclic) joins, a random sample over the join result…
We consider two classes of random graphs: $(a)$ Poissonian random graphs in which the $n$ vertices in the graph have i.i.d.\ weights distributed as $X$, where $\mathbb{E}(X) = \mu$. Edges are added according to a product measure and the…
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation,…
A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…
Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…
Clustering and closure coefficients are among the most widely applied indicators in the description of the topological structure of a network. Many distinct definitions have been proposed over time, particularly in the case of weighted…
Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…
In this paper, we study two examples of minimum weight random graphs with edge constraints. First we consider the complete graph on ${n}$ vertices equipped with uniformly heavy edge weights and use iteration methods to obtain deviation…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
We consider the random connection model in which an edge between two Poisson points at distance $r$ is present with probability $g(r)$. We conduct an extreme value analysis on this model, namely by investigating the longest edge with at…
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
We derive properties of Latent Variable Models for networks, a broad class of models that includes the widely-used Latent Position Models. These include the average degree distribution, clustering coefficient, average path length and degree…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…