相关论文: Identification of critical nodes in large-scale sp…

This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle…

The second smallest eigenvalue of the Laplacian matrix is determinative in characterizing many network properties and is known as algebraic connectivity. In this paper, we investigate the problem of maximizing algebraic connectivity in…

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…

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…

With its origin in sociology, Social Network Analysis (SNA), quickly emerged and spread to other areas of research, including anthropology, biology, information science, organizational studies, political science, and computer science. Being…

For a connected graph $\mathcal{G}=(V,E)$ with $n$ nodes, $m$ edges, and Laplacian matrix $\boldsymbol{{\mathit{L}}}$, a grounded Laplacian matrix $\boldsymbol{{\mathit{L}}}(S)$ of $\mathcal{G}$ is a $(n-k) \times (n-k)$ principal submatrix…

Pinning control of a complex network aims at forcing the states of all nodes to track an external signal by controlling a small number of nodes in the network. In this paper, an algebraic graph-theoretic condition is introduced to optimize…

Network centrality is a foundational concept for quantifying the importance of nodes within a network. Many traditional centrality measures--such as degree and betweenness centrality--are purely structural and often overlook the dynamics…

We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These…

In a network consisting of n nodes, our goal is to identify the most central k nodes with respect to the proposed definitions of centrality. Depending on the specific application, there exist several metrics for quantifying k-centrality,…

The graph identification problem consists of discovering the interactions among nodes in a network given their state/feature trajectories. This problem is challenging because the behavior of a node is coupled to all the other nodes by the…

This paper provides a construction method of the nearest graph Laplacian to a matrix identified from measurement data of graph Laplacian dynamics that include biochemical systems, synchronization systems, and multi-agent systems. We…

We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We define the Laplacian of the graph as dependent on the pairwise distance…

In this article, we illustrate and draw connections between the geometry of zero sets of eigenfunctions, graph theory and the vanishing order of eigenfunctions. We identify the nodal set of an eigenfunction of the Laplacian (with smooth…

Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximising algebraic connectivity both local and globally over all simple, undirected,…

The minimal network problem is a classical topic in geometric measure theory and the calculus of variations, which aims to find networks of minimal length connecting given points. Most classical results are established in the Euclidean…

This paper continues the study of local detectability and observability requirements on components of distributed observers networks to ensure detectability properties of the network. First, we present a sketch of an elementary proof of the…

The connectivity structure of a network can be very sensitive to removal of certain nodes in the network. In this paper, we study the sensitivity of the largest component size to node removals. We prove that minimizing the largest component…

In this paper, we consider the weighted graph matching problem with partially disclosed correspondences between a number of anchor nodes. Our construction exploits recently introduced node signatures based on graph Laplacians, namely the…

An analytic approach is presented to developing exact expressions for the two-point resistance between arbitrary nodes on certain non-regular resistor networks. This generalises previous approaches, which only deliver results for networks…