Related papers: The weighted random graph model
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features,…
In this paper, we derive cumulant bounds for subgraph counts and power-weighted edge length in a class of spatial random networks known as weighted random connection models. This involves dealing with long-range spatial correlations induced…
Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined…
Real-data networks often appear to have strong modularity, or network-of-networks structure, in which subgraphs of various size and consistency occur. Finding the respective subgraph structure is of great importance, in particular for…
In this paper, we propose a multilayer inhomogeneous random graph model (MIRG), whose layers may consist of both single-edge and multi-edge graphs. In the single layer case, it has been shown that the regular variation of the weight…
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…
Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~\cite{mgr, fmk,…
Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Networks representing many complex systems in nature and society share some common structural properties like heterogeneous degree distributions and strong clustering. Recent research on network geometry has shown that those real networks…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
The theory of random graphs goes back to the late 1950s when Paul Erd\H{o}s and Alfr\'ed R\'enyi introduced the Erd\H{o}s-R\'enyi random graph. Since then many models have been developed, and the study of random graph models has become…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
Graph Neural Networks (GNNs) have achieved remarkable success across diverse tasks on graph-structured data, primarily through the use of learned weights in message passing layers. In this paper, we demonstrate that random weights can be…
The geometric renormalization technique for complex networks has successfully revealed the multiscale self-similarity of real network topologies and can be applied to generate replicas at different length scales. In this letter, we extend…