Related papers: A New Notion of Effective Resistance for Directed …
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…
This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…
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 effective resistance between a pair of nodes in a weighted undirected graph is defined as the potential difference induced between them when a unit current is injected at the first node and extracted at the second node, treating edge…
In network theory, the concept of effective resistance is a distance measure on a graph that relates the global network properties to individual connections between nodes. In addition, the Kron reduction method is a standard tool for…
This work presents a new method for symmetrization of directed graphs that constructs an undirected graph with equivalent pairwise effective resistances as a given directed graph. Consequently a graph metric, square root of effective…
The concept of effective resistance, originally introduced in electrical circuit theory, has been extended to the setting of graphs by interpreting each edge as a resistor. In this context, the effective resistance between two vertices…
We completely characterize when the free effective resistance of an infinite graph can be expressed in terms of simple hitting probabilities of the graphs random walk.
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality 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…
We produce a characterization of finite metric spaces which are given by the effective resistance of a graph. This characterization is applied to the more general context of resistance metrics defined by Kigami. A countably infinite…
In this paper we give a survey of methods used to calculate values of resistance distance (also known as effective resistance) in graphs. Resistance distance has played a prominent role not only in circuit theory and chemistry, but also in…
The existing research on robust Graph Neural Networks (GNNs) fails to acknowledge the significance of directed graphs in providing rich information about networks' inherent structure. This work presents the first investigation into the…
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…
We introduce a new arc in directed graphs of integers. Among other things, we determine the positive integers that have arcs to all except a finite number of positive integers. We also propose some possible research problems at the end of…
This paper extends the definitions of effective resistance and effective conductance to characterize the overall relation (positive coupling or antagonism) between any two disjoint sets of nodes in a signed graph. It generalizes the…
An analytical approach is developed to obtain the exact expressions for the two-point resistance, and the total effective resistance of the complete graph minus $N$ edges of the opposite vertices. These expressions are written in terms of…
This is the second report of our work on the construction of directed strongly regular graphs. In our previous work, we constructed a couple of infinite families of new directed strongly regular graphs on the sets of antiflags of partial…
Adversarial attacks to graph analytics are gaining increased attention. To date, two lines of countermeasures have been proposed to resist various graph adversarial attacks from the perspectives of either graph per se or graph neural…
For a simple graph $G=(V,E)$ and edge $e\in E$, the effective resistance is defined as a ratio $\frac{\tau(G/e)}{\tau(G)}$, where $\tau(G)$ denotes the number of spanning trees in $G$. We resolve the inverse problem for the effective…