Related papers: Cumulant method for weighted random connection mod…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
Modeling networks can serve as a means of summarizing high-dimensional complex systems. Adapting an approach devised for dense, weighted networks, we propose a new method for generating and estimating unweighted networks. This approach can…
Consider a set of $n$ vertices, where each vertex has a location in $\mathbb{R}^d$ that is sampled uniformly from the unit cube in $\mathbb{R}^d$, and a weight associated to it. Construct a random graph by placing edges independently for…
Subgraph counting is a fundamental task that underpins several network analysis methodologies, including community detection and graph two-sample tests. Counting subgraphs is a computationally intensive problem. Substantial research has…
For a given homogeneous Poisson point process in $\mathbb{R}^d$ two points are connected by an edge if their distance is bounded by a prescribed distance parameter. The behaviour of the resulting random graph, the Gilbert graph or random…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general…
We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube…
We investigate a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on…
The edges in networks are not only binary, either present or absent, but also take weighted values in many scenarios (e.g., the number of emails between two users). The covariate-$p_0$ model has been proposed to model binary directed…
Longitudinal binary relational data can be better understood by implementing a latent space model for dynamic networks. This approach can be broadly extended to many types of weighted edges by using a link function to model the mean of the…
We investigate random graphs on the points of a Poisson process in $d$-dimensional space, which combine scale-free degree distributions and long-range effects. Every Poisson point carries an independent random mark and given marks and…
We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
We analyze the correlation between randomly chosen edge weights on neighboring edges in a directed graph. This shared-endpoint correlation controls the expected organization of randomly drawn edge flows when the flow on each edge is…
This paper considers limit theorems associated with subgraph counts in the age-dependent random connection model. First, we identify regimes where the count of sub-trees converges weakly to a stable random variable under suitable…
Consider a stationary Poisson point process in $\mathbb{R}^d$ and connect any two points whenever their distance is less than or equal to a prescribed distance parameter. This construction gives rise to the well known random geometric…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…