Related papers: Cut-edge centralities in an undirected graph
On finite metric graphs the set of all realizations of the Laplace operator in the edgewise defined $L^2$-spaces are studied. These are defined by coupling boundary conditions at the vertices most of which define non-self-adjoint operators.…
We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees.
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
The multi-commodity flow-cut gap is a fundamental parameter that affects the performance of several divide \& conquer algorithms, and has been extensively studied for various classes of undirected graphs. It has been shown by Linial, London…
This paper proposes a simple procedure to decide whether the empirically-observed adjacency or weights matrix, which characterizes the graph underlying a socio-economic network, is sufficiently symmetric (respectively, asymmetric) to…
We analyze the single particle states at the edges of disordered graphene quantum dots. We show that generic graphene quantum dots support a number of edge states proportional to circumference of the dot over the lattice constant. Our…
Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was…
We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward $p$-stars. Our models are close cousins of exponential random graph models (ERGMs), in which edges and certain other subgraph…
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…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
The present study was concerned with network failure problems for simple connected undirected graphs. A connected graph becomes unconnected through edge failure, under the assumptions that only edges can fail and each edge has an identical…
We prove that there is a unique graph with four edges which is the Gruenberg-Kegel graph of a solvable cut group. This contributes to the classification of the Gruenberg-Kegel graphs of solvable cut groups initiated in [A. B\"achle, A.…
In this paper we study the inverse eigenvector centrality problem on directed graphs: given a prescribed node centrality profile, we seek edge weights that realize it. Since this inverse problem generally admits infinitely many solutions,…
Confirming a conjecture posed by Caro, it was shown by Chen and Yu that every graph $G$ with $n$ vertices and at most $2n-4$ edges has a stable cutset, which is a stable set of vertices whose removal disconnects the graph. Le and Pfender…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
We study the directed maximum common edge subgraph problem (DMCES) for the class of directed graphs that are finite, weakly connected, oriented, and simple. We use DMCES to define a metric on partially ordered sets that can be represented…
We study property testing of (di)graph properties in bounded-degree graph models. The study of graph properties in bounded-degree models is one of the focal directions of research in property testing in the last 15 years. However, despite…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
The topological structure of complex networks has fascinated researchers for several decades, resulting in the discovery of many universal properties and reoccurring characteristics of different kinds of networks. However, much less is…
We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…