相关论文: Average resistance of toroidal graphs
Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbours to each point of a dataset to perform their tasks. These proximity relations define a so-called…
A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative…
It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher-order nonpairwise relations among nodes, i.e., interactions between among than two nodes at a time. This…
We define and study two new kinds of "effective resistances" based on hubs-biased -- hubs-repelling and hubs-attracting -- models of navigating a graph/network. We prove that these effective resistances are squared Euclidean distances…
Given the ensemble of random Gaussian Laplace eigenfunctions on the three-dimensional torus (`3d arithmetic random waves'), we investigate the $1$-dimensional Hausdorff measure of the nodal intersection curve against a compact regular toral…
The reciprocal degree resistance distance index of a connected graph $G$ is defined as $RDR(G)=\sum\limits_{\{u,v\}\subseteq V(G)}\frac {d_G(u)+d_G(v)}{r_G(u,v)}$, where $r_G(u,v)$ is the resistance distance between vertices $u$ and $v$ in…
We consider the problem of diffusing information in networks that contain malicious nodes. We assume that each normal node in the network has no knowledge of the network topology other than an upper bound on the number of malicious nodes in…
In this paper, we present two new matrices, namely the resistance Laplacian and resistance signless Laplacian matrix of a connected graph. We provide a generalized form of these matrices for different classes of graphs, including the…
A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and 1<p<\infty. Generalisations are obtained for the Laman and…
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
In this paper we deal with the notion of the effective impedance of AC networks consisting of resistances, coils and capacitors. Mathematically such a network is a locally finite graph whose edges are endowed with complex-valued weights…
We study the nodal intersections number of random Gaussian toral Laplace eigenfunctions ("arithmetic random waves") against a fixed smooth reference curve. The expected intersection number is proportional to the the square root of the…
A comparison between the topological properties of the measured Internet topology, at the autonomous system level (AS graph), and the equivalent graphs generated by two different power law topology generators is presented. Only one of the…
Let $G$ be a connected graph with $V(G)=\{1,\dotsc,n\}$. Then the resistance distance between any two vertices $i$ and $j$ is given by $r_{ij}:=l_{ii}^{\dag} + l_{jj}^{\dag}-2 l_{ij}^{\dag}$, where $l_{ij}^\dag$ is the $(i,j)^{\rm th}$…
For random $d$-regular graphs on $N$ vertices with $1 \ll d \ll N^{2/3}$, we develop a $d^{-1/2}$ expansion of the local eigenvalue distribution about the Kesten-McKay law up to order $d^{-3}$. This result is valid up to the edge of the…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…