Related papers: Boundary value problems in consensus networks

Consensus dynamics support decentralized machine learning for data that is distributed across a cloud compute cluster or across the internet of things. In these and other settings, one seeks to minimize the time $\tau_\epsilon$ required to…

The threshold network model is a type of finite random graphs. In this paper, we introduce a generalized threshold network model. A pair of vertices with random weights is connected by an edge when real-valued functions of the pair of…

Overlapping communities are key characteristics of the structure and function analysis of complex networks. Shared or overlapping nodes within overlapping communities can form either subcommunities or act as intersections between larger…

A reliable inference of networks from data is of key interest in the Neurosciences. Several methods have been suggested in the literature to reliably determine links in a network. To decide about the presence of links, these techniques rely…

The increasing complexity and interdependency of today's networks highlight the importance of studying network robustness to failure and attacks. Many large-scale networks are prone to cascading effects where a limited number of initial…

The paper considers the consensus problem in large networks represented by time-varying directed graphs. A practical way of dealing with large-scale networks is to reduce their dimension by collapsing the states of nodes belonging to…

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…

In wireless networks, the knowledge of nodal distances is essential for several areas such as system configuration, performance analysis and protocol design. In order to evaluate distance distributions in random networks, the underlying…

Graph Neural Networks (GNNs) have improved unsupervised community detection of clustered nodes due to their ability to encode the dual dimensionality of the connectivity and feature information spaces of graphs. Identifying the latent…

Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A common example is the geographic position: one may uncover communities in a network of…

Individuals who interact with each other in social networks often exchange ideas and influence each other's opinions. A popular approach to study the spread of opinions on networks is by examining bounded-confidence models (BCMs), in which…

We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…

We study norm-based uniform convergence bounds for neural networks, aiming at a tight understanding of how these are affected by the architecture and type of norm constraint, for the simple class of scalar-valued one-hidden-layer networks,…

It is commonly accepted that some phenomena are social: for example, individuals' smoking habits often correlate with those of their peers. Such correlations can have a variety of explanations, such as direct contagion or shared…

A fundamental problem in the study of networks is the identification of important nodes. This is typically achieved using centrality metrics, which rank nodes in terms of their position in the network. This approach works well for static…

Wireless networks are fundamentally limited by the intensity of the received signals and by their inherent interference. It is shown here that in finite ad hoc networks where node placement is modelled according to a Poisson point process…

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate…

In this paper, we study the crucial elements of complex networks, namely nodes, and edges and their properties such as their community structure, which play an important role in dictating the robustness of the network towards structural…

We consider the problems of reaching average consensus and solving consensus-based optimization over unreliable communication networks wherein packets may be dropped accidentally during transmission. Existing work either assumes that the…

Sensor networks potentially feature large numbers of nodes that can sense their environment over time, communicate with each other over a wireless network, and process information. They differ from data networks in that the network as a…