Related papers: Monotonicity properties of exclusion sensitivity
Recently the study of noise sensitivity and noise stability of Boolean functions has received considerable attention. The purpose of this paper is to extend these notions in a natural way to a different class of perturbations, namely those…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many…
This paper presents a formal definition of stability for node centrality measures in weighted graphs. It is shown that the commonly used measures of degree, closeness and eigenvector centrality are stable whereas betweenness centrality is…
Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…
During the past 15 years, several extensions of the concepts noise sensitivity and noise stability, first coined in~\cite{schramm2000}, has been studied. The purpose in this paper is to give definitions of this concepts in the setting of…
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths…
Graph convolutional neural networks (GCNNs) are nonlinear processing tools to learn representations from network data. A key property of GCNNs is their stability to graph perturbations. Current analysis considers deterministic perturbations…
Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…
Learning low-dimensional representations on graphs has proved to be effective in various downstream tasks. However, noises prevail in real-world networks, which compromise networks to a large extent in that edges in networks propagate…
The Rayleigh monotonicity is a principle from the theory of electrical networks. Its combinatorial interpretation says for each two edges of a graph G, that the presence of one of them in a random spanning tree of G is negatively correlated…
A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative…
The query complexity of graph properties is well-studied when queries are on edges. We investigate the same when queries are on nodes. In this setting a graph $G = (V, E)$ on $n$ vertices and a property $\mathcal{P}$ are given. A black-box…
Network data can be conveniently modeled as a graph signal, where data values are assigned to the nodes of a graph describing the underlying network topology. Successful learning from network data requires methods that effectively exploit…
A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where…
Graph-based learning is a rapidly growing sub-field of machine learning with applications in social networks, citation networks, and bioinformatics. One of the most popular models is graph attention networks. They were introduced to allow a…
Given that no existing graph construction method can generate a perfect graph for a given dataset, graph-based algorithms are often affected by redundant and erroneous edges present within the constructed graphs. In this paper, we view…
Chains are vector-valued signals sampling a curve. They are important to motion signal processing and to many scientific applications including location sensors. We propose a novel measure of smoothness for chains curves by generalizing the…
The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…