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We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized…

We consider the problem of information aggregation in sensor networks, where one is interested in computing a function of the sensor measurements. We allow for block processing and study in-network function computation in directed graphs…

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper…

In this paper, various kinds of invariants of directed graphs are summarized. In the first topic, the invariant w(G) for a directed graph G is introduced, which is primarily defined by S. Chen and X.M. Chen to solve a problem of weak…

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks…

The problem of achieving consensus in a network of connected systems arises in many science and engineering applications. In contrast to previous works, we focus on the system reactivity, i.e., the initial amplification of the norm of the…

The network structure of an urban transportation system has a significant impact on its traffic performance. This study uses network indicators along with several traffic performance measures including speed, trip length, travel time, and…

In this paper, we study dual quaternion and dual complex unit gain graphs and their spectral properties in a unified frame of dual unit gain graphs. Unit dual quaternions represent rigid movements in the 3D space, and have wide applications…

In an intelligent transportation system, the effects and relations of traffic flow at different points in a network are valuable features which can be exploited for control system design and traffic forecasting. In this paper, we define the…

Recent spectral graph sparsification research allows constructing nearly-linear-sized subgraphs that can well preserve the spectral (structural) properties of the original graph, such as the first few eigenvalues and eigenvectors of the…

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).…

Graph heterophily poses a formidable challenge to the performance of Message-passing Graph Neural Networks (MP-GNNs). The familiar low-pass filters like Graph Convolutional Networks (GCNs) face performance degradation, which can be…

This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…

The second-largest eigenvalue and second-smallest Laplacian eigenvalue of a graph are measures of its connectivity. These eigenvalues can be used to analyze the robustness, resilience, and synchronizability of networks, and are related to…

In this paper, we design distributed multi-modal localization approaches for Connected and Automated vehicles. We utilize information diffusion on graphs formed by moving vehicles, based on Adapt-then-Combine strategies combined with the…

Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier transform and then…

Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and…

In this paper we investigated the possibility to use the magnetic Laplacian to characterize directed graphs (a.k.a. networks). Many interesting results are obtained, including the finding that community structure is related to rotational…

The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…

We investigate the distributed multi-agent sharing optimization problem in a directed graph, with a composite objective function consisting of a smooth function plus a convex (possibly non-smooth) function shared by all agents. While…