Related papers: Spectral Heuristics Applied to Vertex Reliability
In recent times, the functioning of various aspects of modern society---ranging from the various infrastructural utilities such as electrical power, water to socio-economical aspects such as telecommunications, business, commerce,…
The approximate computation of twin-width has attracted significant attention already since the moment the parameter was introduced. A recently proposed approach (STACS 2024) towards obtaining a better understanding of this question is to…
In this work, water distribution systems are regarded as large sparse planar graphs with complex network characteristics and the relationship between important topological features of the network (i.e. structural robustness and loop…
Hypergraphs require higher-dimensional representations, which makes it more difficult to compute and interpret their spectral properties. This survey article uses the framework of hypermatrices to give an in-depth overview of the spectral…
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the…
We present a new, novel approach to obtaining a network's connectivity. More specifically, we show that there exists a relationship between a network's graph isoperimetric properties and its conditional connectivity. A network's…
For a network consisting of a graph with edge weights prescribed by a given conductance function $c$, we consider the effects of replacing these weights with a new function $b$ that satisfies $b \leq c$ on each edge. In particular, we…
This paper introduces several techniques that improve the scalability of the deductive verification of data-level programs working on arrays and matrices. First of all, we introduce a technique to rewrite expressions with (nested)…
We consider the problem of characterizing graphs with the maximum spectral radius among the connected graphs with given numbers of vertices and edges. It is well-known that the candidates for extremal graphs are threshold graphs, but only a…
In this note, we show that three graph properties - strong connectivity, acyclicity, and reachability from a vertex $s$ to all vertices - each require a working memory of $\Omega (\epsilon m)$ on a graph with $m$ edges to be determined…
In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…
Wireless network topologies change over time and maintaining routes requires frequent updates. Updates are costly in terms of consuming throughput available for data transmission, which is precious in wireless networks. In this paper, we…
In recent years, the notion of r-robustness for the communication graph of the network has been introduced to address the challenge of achieving consensus in the presence of misbehaving agents. Higher r-robustness typically implies higher…
A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble…
A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability $p$. One can ask for the probability that all vertices can communicate ({\em all-terminal…
The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations,…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
Graph edge perturbations are dedicated to damaging the prediction of graph neural networks by modifying the graph structure. Previous gray-box attackers employ gradients from the surrogate model to locate the vulnerable edges to perturb the…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…