Related papers: Spectral Heuristics Applied to Vertex Reliability
Rapid reliability assessment of transportation networks can enhance preparedness, risk mitigation, and response management procedures related to these systems. Network reliability analysis commonly considers network-level performance and…
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the…
Complex networks or graphs are ubiquitous in sciences and engineering: biological networks, brain networks, transportation networks, social networks, and the World Wide Web, to name a few. Spectral graph theory provides a set of useful…
With the rapid growth of online social networks, strengthening their stability has emerged as a key research focus. This study aims to identify influential relationships that significantly impact community stability. In this paper, we…
Vertex similarity is a major problem in network science with a wide range of applications. In this work we provide novel perspectives on finding (dis)similar vertices within a network and across two networks with the same number of vertices…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
Over the recent years, Graph Neural Networks have become increasingly popular in network analytic and beyond. With that, their architecture noticeable diverges from the classical multi-layered hierarchical organization of the traditional…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
Network-topology inference from (vertex) signal observations is a prominent problem across data-science and engineering disciplines. Most existing schemes assume that observations from all nodes are available, but in many practical…
The spectral gap for Laplace operators on metric graphs is investigated in relation to graph's connectivity, in particular what happens if an edge is added to (or deleted from) a graph. It is shown that in contrast to discrete graphs…
Vertex connectivity is a well-studied concept in graph theory with numerous applications. A graph is $k$-connected if it remains connected after removing any $k-1$ vertices. The vertex connectivity of a graph is the maximum $k$ such that…
In this paper we present a general procedure that allows for the reduction or expansion of any network (considered as a weighted graph). This procedure maintains the spectrum of the network's adjacency matrix up to a set of eigenvalues…
Including intricate topological information (e.g., cycles) provably enhances the expressivity of message-passing graph neural networks (GNNs) beyond the Weisfeiler-Leman (WL) hierarchy. Consequently, Persistent Homology (PH) methods are…
Neural networks (NNs) are increasingly applied in safety-critical systems such as autonomous vehicles. However, they are fragile and are often ill-behaved. Consequently, their behaviors should undergo rigorous guarantees before deployment…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
Network architecture design is very important for the optimization of industrial networks. The type of network architecture can be divided into small-scale network and large-scale network according to its scale. Graph theory is an efficient…
Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant…
This paper formulates a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. The smoothness condition…