Related papers: Warning Propagation: stability and subcriticality
Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each…
Recent years have seen a growing interest in the use of belief propagation - an algorithm originally introduced for performing statistical inference on graphical models - for approximate, but highly efficient, tensor network contraction.…
Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…
The algorithms based on message passing neural networks (MPNNs) on graphs have recently achieved great success for various graph applications. However, studies find that these methods always propagate the information to very limited…
Graph Neural Networks (GNNs), originally proposed for node classification, have also motivated many recent works on edge prediction (a.k.a., link prediction). However, existing methods lack elaborate design regarding the distinctions…
This work develops a flexible and mathematically sound framework for the design and analysis of graph scattering networks with variable branching ratios and generic functional calculus filters. Spectrally-agnostic stability guarantees for…
We consider a scenario of broadcasting information over a network of nodes connected by noiseless communication links. A source node in the network has $k$ data packets to broadcast, and it suffices that a large fraction of the network…
This paper presents a randomized self-stabilizing algorithm that elects a leader $r$ in a general $n$-node undirected graph and constructs a spanning tree $T$ rooted at $r$. The algorithm works under the synchronous message passing network…
In this paper, we study PUSH-PULL style rumor spreading algorithms in the mobile telephone model, a variant of the classical telephone model in which each node can participate in at most one connection per round; i.e., you can no longer…
Graph neural networks (GNNs) have evolved into one of the most popular deep learning architectures. However, GNNs suffer from over-smoothing node information and, therefore, struggle to solve tasks where global graph properties are…
Social networks are frequently polluted by rumors, which can be detected by advanced models such as graph neural networks. However, the models are vulnerable to attacks and understanding the vulnerabilities is critical to rumor detection in…
Graph Neural Networks (GNNs) have seen significant advances in recent years, yet their application to multigraphs, where parallel edges exist between the same pair of nodes, remains under-explored. Standard GNNs, designed for simple graphs,…
In the problem of structured prediction with graph representation learning (GRL for short), the hypothesis returned by the algorithm maps the set of features in the \emph{receptive field} of the targeted vertex to its label. To understand…
We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs), which we call a Hyper-graph Expansion Neural Network (HENN), and provide the first bounds on the stability and transferability…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
We establish a bound for the classic PUSH-PULL rumor spreading protocol on arbitrary graphs, in terms of the vertex expansion of the graph. We show that O(log^2(n)/\alpha) rounds suffice with high probability to spread a rumor from a single…
We study a distributed consensus problem on a complete communication network of $n$ vertices, each holding one of two opinions. The vertices communicate in rounds, possibly in the presence of adversarial noise, and exchange information…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…