Related papers: Minimizing the effective graph resistance by addin…
Graph-based indexes have been widely employed to accelerate approximate similarity search of high-dimensional vectors. However, the performance of graph indexes to answer different queries varies vastly, leading to an unstable quality of…
Computing the number of realizations of a minimally rigid graph is a notoriously difficult problem. Towards this goal, for graphs that are minimally rigid in the plane, we take advantage of a recently published algorithm, which is the…
The \emph{$k$-restricted edge-connectivity} of a graph $G$, denoted by $\lambda_k(G)$, is defined as the minimum size of an edge set whose removal leaves exactly two connected components each containing at least $k$ vertices. This graph…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
We study the problem of extracting a selective connector for a given set of query vertices $Q \subseteq V$ in a graph $G = (V,E)$. A selective connector is a subgraph of $G$ which exhibits some cohesiveness property, and contains the query…
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…
Network robustness research aims at finding a measure to quantify network robustness. Once such a measure has been established, we will be able to compare networks, to improve existing networks and to design new networks that are able to…
As a result of the interaction of rapid development and competition in information technologies, the reliability of a network and how solid it remains is important. It is called the hat vulnerability of the network to measure the endurance…
The subdivision graph $S(G)$ of a graph $G$ is the graph obtained by inserting a new vertex into every edge of $G$. In $\cite{PL}$, two classes of new corona graphs, the corona-vertex of the subdivision graph $G_{1}\diamondsuit G_{2}$ and…
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…
Cascading failures are the typical reasons of black- outs in power grids. The grid topology plays an important role in determining the dynamics of cascading failures in power grids. Measures for vulnerability analysis are crucial to assure…
Graph neural networks (GNNs) are the predominant architecture for learning over graphs. As with any machine learning model, an important issue is the detection of attacks, where an adversary can change the output with a small perturbation…
Effective resistances are ubiquitous in graph algorithms and network analysis. In this work, we study sublinear time algorithms to approximate the effective resistance of an adjacent pair $s$ and $t$. We consider the classical adjacency…
Network reliability is an important metric to evaluate the connectivity among given vertices in uncertain graphs. Since the network reliability problem is known as #P-complete, existing studies have used approximation techniques. In this…
Computer or communication networks are so designed that they do not easily get disrupted under external attack and, moreover, these are easily reconstructible if they do get disrupted. These desirable properties of networks can be measured…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
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…
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 $\Lambda(T)$ denote the set of leaves in a tree $T$. One natural problem is to look for a spanning tree $T$ of a given graph $G$ such that $\Lambda(T)$ is as large as possible. This problem is called maximum leaf number, and it is a…
Metros (heavy rail transit systems) are integral parts of urban transportation systems. Failures in their operations can have serious impacts on urban mobility, and measuring their robustness is therefore critical. Moreover, as physical…