Related papers: Convergence Analysis of Signed Nonlinear Networks
We introduce a simple network formation model for social networks. Agents are nodes, connecting to another agent by building a directed edge (or accepting a connection from another agent) has a cost, and reaching (or being reached by) other…
Signed network embedding is an approach to learn low-dimensional representations of nodes in signed networks with both positive and negative links, which facilitates downstream tasks such as link prediction with general data mining…
Studying significant network patterns, known as graphlets (or motifs), has been a popular approach to understand the underlying organizing principles of complex networks. Statistical significance is routinely assessed by comparing to null…
Network embedding is aimed at mapping nodes in a network into low-dimensional vector representations. Graph Neural Networks (GNNs) have received widespread attention and lead to state-of-the-art performance in learning node representations.…
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the…
This paper aims at addressing distributed averaging problems for signed networks in the presence of general directed topologies that are represented by signed digraphs. A new class of improved Laplacian potential functions is proposed by…
Graph convolutional networks (GCNs) are vulnerable to perturbations of the graph structure that are either random, or, adversarially designed. The perturbed links modify the graph neighborhoods, which critically affects the performance of…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
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…
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…
Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…
A main puzzle of deep networks revolves around the absence of overfitting despite large overparametrization and despite the large capacity demonstrated by zero training error on randomly labeled data. In this note, we show that the dynamics…
Given a resistive electrical network, we would like to determine whether all the resistances (edges) in the network are working, and if not, identify which edge (or edges) are faulty. To make this determination, we are allowed to measure…
Contrasts with existing works which all consider nodes as functions and use edges to represent the relationships between different functions. We target at network modeling whose edges are functional data and transform the adjacency matrix…
Networks provide useful tools for analyzing diverse complex systems from natural, social, and technological domains. Growing size and variety of data such as more nodes and links and associated weights, directions, and signs can provide…
Is the enemy of an enemy necessarily a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be "balanced" were…
Graph or network data is ubiquitous in the real world, including social networks, information networks, traffic networks, biological networks and various technical networks. The non-Euclidean nature of graph data poses the challenge for…
The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a…
Lots of neural network architectures have been proposed to deal with learning tasks on graph-structured data. However, most of these models concentrate on only node features during the learning process. The edge features, which usually play…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…