Related papers: Node Reliability: Approximation, Upper Bounds, and…
In many real applications that use and analyze networked data, the links in the network graph may be erroneous, or derived from probabilistic techniques. In such cases, the node classification problem can be challenging, since the…
Our original paper \cite{VanMieghem2025} described the stochastic approximation $\overline{rel}_G(p)=\bigl[1-\phi_D(1-p)\bigr]^{N}$ in \cite[eq. (2.2)]{VanMieghem2025} and the first-order approximation…
Computing the reliability of a time-varying network, taking into account its dynamic nature, is crucial for networks that change over time, such as space networks, vehicular ad-hoc networks, and drone networks. These networks are modeled…
We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in…
Graph neural networks are experiencing a surge of popularity within the machine learning community due to their ability to adapt to non-Euclidean domains and instil inductive biases. Despite this, their stability, i.e., their robustness to…
Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When…
Node-connectivity augmentation is a fundamental network design problem. We are given a $k$-node connected graph $G$ together with an additional set of links, and the goal is to add a cheap subset of links to $G$ to make it $(k+1)$-node…
The network unreliability problem asks for the probability that a given undirected graph gets disconnected when every edge independently fails with a given probability $p$. Valiant (1979) showed that this problem is \#P-hard; therefore, the…
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…
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…
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to…
We consider a large random network, in which the performance of a node depends upon that of its neighbours and some external random influence factors. This results in random vector valued fixed-point (FP) equations in large dimensional…
Subgraphs such as cliques, loops and stars form crucial connections in the topologies of real-world networks. Random graph models provide estimates for how often certain subgraphs appear, which in turn can be tested against real-world…
In this paper, we investigate the exact asymptotic behavior of the connectivity probability in the Erdos-Renyi graph G(n,p), under different asymptotic assumptions on the edge probability p=p(n). We propose a novel approach based on the…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained…
Despite the recently exhibited importance of higher-order interactions for various processes, few flexible (null) models are available. In particular, most studies on hypergraphs focus on a small set of theoretical models. Here, we…
Graph neural networks are becoming increasingly popular in the field of machine learning due to their unique ability to process data structured in graphs. They have also been applied in safety-critical environments where perturbations…
Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against…
Signed graphs are widely used to analyze complex systems such as social, political, and biological networks. The notion of balance, a key concept of signed graphs, reflects the stability of relationships. While it has been extensively…