Related papers: Algorithmic techniques for finding resistance dist…
This paper presents an introduction and expository account of a beautiful, current, and active application of recursions to the computation of resistance distance. Resistance distance, also referred to as effective resistance, is a…
Resistance distance has been studied extensively in the past years, with the majority of previous studies devoted to undirected networks, in spite of the fact that various realistic networks are directed. Although several generalizations of…
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…
Effective resistance is a distance between vertices of a graph that is both theoretically interesting and useful in applications. We study a variant of effective resistance called the biharmonic distance. While the effective resistance…
For a connected graph $G$, its resistance distance matrix is denoted by $R(G)$. A graph is called resistance regular if all the row (or column) sums of $R(G)$ are equal. We provide a necessary and sufficient condition for a simple connected…
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of…
Effective resistance, which originates from the field of circuits analysis, is an important graph distance in spectral graph theory. It has found numerous applications in various areas, such as graph data mining, spectral graph…
In Part I of this work we defined a generalization of the concept of effective resistance to directed graphs, and we explored some of the properties of this new definition. Here, we use the theory developed in Part I to compute effective…
Let $G=(V(G),E(G))$ be a graph with vertex set $V(G)$ and edge set $E(G)$. The resistance distance $R_G(x,y)$ between two vertices $x,y$ of $G$ is defined to be the effective resistance between the two vertices in the corresponding…
Refining previous results, we establish a sharp asymptotic estimate on the expected graph distance between the origin and the terminal point of the trace of the first $n$ steps of the walk. A similar conclusion is drawn for the resistance…
Let $r(u,v)$ be the resistance distance between two vertices $u, v$ of a simple graph $G$, which is the effective resistance between the vertices in the corresponding electrical network constructed from $G$ by replacing each edge of $G$…
In this article we consider resistance matrix of a connected graph. For unweighted graph we study some necessary and sufficient conditions for resistance regular graphs. Also we find some relationship between Laplacian matrix and resistance…
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigen-vectors of the graph Laplacian. Graph laplacians are used to find low dimensional structures in high…
We obtain a general formula for the resistance distance (or effective resistance) between any pair of nodes in a general family of graphs which we call flower graphs. Flower graphs are obtained from identifying nodes of multiple copies of a…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
Metric graphs are ubiquitous in science and engineering. For example, many data are drawn from hidden spaces that are graph-like, such as the cosmic web. A metric graph offers one of the simplest yet still meaningful ways to represent the…
Let $G$ be a connected graph. The resistance distance between two vertices $u$ and $v$ of $G$, denoted by $R_{G}[u,v]$, is defined as the net effective resistance between them in the electric network constructed from $G$ by replacing each…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper. Our main result, Theorem 4, shows(together with Corollary 3) that if distance is measured by the electric resistance…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…