Related papers: A study on resistance matrix of graphs
We investigate the torsion function or landscape function and its integral, the torsional rigidity, of Laplacians on metric graphs subject to $\delta$-vertex conditions. A variational characterization of torsional rigidity and Hadamard-type…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
Several researchers have recently explored various graph parameters that can or cannot be characterized by the spectrum of a matrix associated with a graph. In this paper we show that several NP-hard zero forcing numbers are not…
We present enumeration results on the number of connected graphs up to 10 vertices for which there is at least one other graph with the same spectrum (a cospectral mate), or at least one other graph with the same Smith normal form…
We investigate the problem of learning undirected graphical models under Laplacian structural constraints from the point of view of financial market data. We show that Laplacian constraints have meaningful physical interpretations related…
We use the line digraph construction to associate an orthogonal matrix with each graph. From this orthogonal matrix, we derive two further matrices. The spectrum of each of these three matrices is considered as a graph invariant. For the…
Although research on the control of networked systems has grown considerably, graph-theoretic and algorithmic studies on matrix-weighted graphs remain limited. To bridge this gap in the literature, this work introduces two algorithms-the…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
A graph is an opposition graph, respectively, a coalition graph, if it admits an acyclic orientation which puts the two end-edges of every chordless 4-vertex path in opposition, respectively, in the same direction. Opposition and coalition…
There has been recent growing interest in graph theoretical properties known as r- and (r,s)-robustness. These properties serve as sufficient conditions guaranteeing the success of certain consensus algorithms in networks with misbehaving…
Recently, several data analytic techniques based on connection graph laplacian (CGL) ideas have appeared in the literature. At this point, the properties of these methods are starting to be understood in the setting where the data is…
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…
Threshold graphs are generated from one node by repeatedly adding a node that links to all existing nodes or adding a node without links. In the weighted threshold graph, we add a new node in step $i$, which is linked to all existing nodes…
It is reported that dynamical systems over digraphs have superior performance in terms of system damping and tolerance to time delays if the underlying graph Laplacian has a purely real spectrum. This paper investigates the topological…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
The aim of the present article is to give an overview of spectral theory on metric graphs guided by spectral geometry on discrete graphs and manifolds. We present the basic concept of metric graphs and natural Laplacians acting on it and…
We define the notion of affine rigidity of a hypergraph and prove a variety of fundamental results for this notion. First, we show that affine rigidity can be determined by the rank of a specific matrix which implies that affine rigidity is…
This paper addresses questions regarding controllability for `generic parameter' dynamical systems, i.e. the question whether a dynamical system is `structurally controllable'. Unlike conventional methods that deal with structural…
This paper deals with identifiability of undirected dynamical networks with single-integrator node dynamics. We assume that the graph structure of such networks is known, and aim to find graph-theoretic conditions under which the state…