Related papers: Controllability Analysis of Threshold Graphs and C…
Selecting informative nodes over large-scale networks becomes increasingly important in many research areas. Most existing methods focus on the local network structure and incur heavy computational costs for the large-scale problem. In this…
The Laplacian matrix of a simple graph is the difference of the diagonal matrix of vertex degree and the (0,1) adjacency matrix. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been…
Renormalization of complex networks requires principled criteria for assessing whether a coarse-graining preserves dynamical content. We prove that discrete harmonic morphisms -- surjective maps preserving harmonic functions -- provide the…
It is well-known that the eigenvalue spectrum of the Laplacian matrix of a network contains valuable information about the network structure and the behavior of many dynamical processes run on it. In this paper, we propose a fully…
This paper investigates the finite-horizon optimal control (FHOC) problem of Boolean control networks (BCNs) from a graph theory perspective. We first formulate two general problems to unify various special cases studied in the literature:…
Though commonly found in the real world, directed networks have received relatively less attention from the literature in which concerns their topological and dynamical characteristics. In this work, we develop a magnetic Laplacian-based…
To achieve control objectives for extremely large-scale complex networks using standard methods is essentially intractable. In this work a theory of the approximate control of complex network systems is proposed and developed by the use of…
We propose a structure-preserving model-reduction methodology for large-scale dynamic networks with tightly-connected components. First, the coherent groups are identified by a spectral clustering algorithm on the graph Laplacian matrix…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
Convolutional layers within graph neural networks operate by aggregating information about local neighbourhood structures; one common way to encode such substructures is through random walks. The distribution of these random walks evolves…
Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density…
The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is…
We present a framework based on spectral graph theory that captures the interplay among network topology, system inertia, and generator and load damping in determining the overall grid behavior and performance. Specifically, we show that…
Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…
How to obtain a graph from data samples is an important problem in graph signal processing. One way to formulate this graph learning problem is based on Gaussian maximum likelihood estimation, possibly under particular topology constraints.…
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…
Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of…
In this paper, we consider a network of agents with Laplacian dynamics, and study the problem of improving network robustness by adding a maximum number of edges within the network while preserving a lower bound on its strong structural…
Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…
Graph neural networks process information on graphs represented at a given resolution scale. We analyze the effect of using different coarse-grained graph resolutions, obtained through the Laplacian renormalization group theory, on node…