Related papers: Graph-theoretic optimization for edge consensus
We describe a synchronous distributed algorithm which identifies the edge-biconnected components of a connected network. It requires a leader, and uses messages of size O(log |V|). The main idea is to preorder a BFS spanning tree, and then…
Modularity maximization is one of the state-of-the-art methods for community detection that has gained popularity in the last decade. Yet it suffers from the resolution limit problem by preferring under certain conditions large communities…
We investigate the vulnerabilities of consensus-based distributed optimization protocols to nodes that deviate from the prescribed update rule (e.g., due to failures or adversarial attacks). We first characterize certain fundamental…
We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the…
Graph signals are functions of the underlying graph. When the edge-weight between a pair of nodes is high, the corresponding signals generally have a higher correlation. As a result, the signals can be represented in terms of a graph-based…
Stabilization of graphs has received substantial attention in recent years due to its connection to game theory. Stable graphs are exactly the graphs inducing a matching game with non-empty core. They are also the graphs that induce a…
In this paper a tight lower bound for algebraic connectivity of graphs (second smallest eigenvalue of the Laplacian matrix of the graph) based on connection-graph-stability method is introduced. The connection-graph-stability score for each…
A graph is $2$-planar if it has local crossing number two, that is, it can be drawn in the plane such that every edge has at most two crossings. A graph is maximal $2$-planar if no edge can be added such that the resulting graph remains…
When processing a batch of graphs in machine learning models such as Graph Neural Networks (GNN), it is common to combine several small graphs into one overall graph to accelerate processing and remove or reduce the overhead of padding.…
The transient response of power grids to external disturbances influences their stable operation. This paper studies the effect of topology in linear time-invariant dynamics of different power grids. For a variety of objective functions, a…
The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a…
Adding edges between layers of interconnected networks is an important way to optimize the spreading dynamics. While previous studies mostly focus on the case of adding a single edge, the theoretical optimal strategy for adding multiple…
The `Signal plus Noise' model for nonparametric regression can be extended to the case of observations taken at the vertices of a graph. This model includes many familiar regression problems. This article discusses the use of the edges of a…
Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs,…
Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the…
Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…
A monitoring edge-geodetic set (or meg-set for short) of a graph is a set of vertices $M$ such that if any edge is removed, then the distance between some two vertices of $M$ increases. This notion was introduced by Foucaud et al. in 2023…
In this paper, we use the H2 norm associated with a communication graph to characterize the robustness of consensus to noise. In particular, we restrict our attention to trees and by systematic attention to the effect of local changes in…
Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real…
Graph neural networks (GNNs) are the dominant approach to solving machine learning problems defined over graphs. Despite much theoretical and empirical work in recent years, our understanding of finer-grained aspects of architectural design…