English
Related papers

Related papers: From Graph Isoperimetric Inequality to Network Con…

200 papers

Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…

Databases · Computer Science 2020-05-26 Xiangyu Ke , Arijit Khan , Mohammad Al Hasan , Rojin Rezvansangsari

The neighbor connectivity of a graph $G$ is the least number of vertices such that removing their closed neighborhoods from $G$ results in a graph that is disconnected, complete or empty. If a~graph is used to model the topology of an…

Discrete Mathematics · Computer Science 2019-10-29 Tomáš Dvořák , Mei-Mei Gu

This article investigates the connectivity dimension of a graph. We introduce this concept in analogy to the metric dimension of a graph, providing a graph parameter that measures the heterogeneity of the connectivity structure of a graph.…

Combinatorics · Mathematics 2025-08-14 Kurt Klement Gottwald , Tobias Hofmann

In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…

Data Structures and Algorithms · Computer Science 2018-03-01 Loukas Georgiadis , Giuseppe F. Italiano , Nikos Parotsidis

As a generalization of the traditional connectivity, the g-component edge connectivity c{\lambda}g(G) of a non-complete graph G is the minimum number of edges to be deleted from the graph G such that the resulting graph has at least g…

Combinatorics · Mathematics 2021-05-12 Dong Liu , Pingshan Li , Bicheng Zhang

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…

Optimization and Control · Mathematics 2015-03-03 Daniel Zelazo , Mathias Bürger

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…

Discrete Mathematics · Computer Science 2013-11-21 W. Ellens , R. E. Kooij

Graphs are pervasive in our everyday lives, with relevance to biology, the internet, and infrastructure, as well as numerous other applications. It is thus necessary to have an understanding as to how quickly a graph disintegrates, whether…

Social and Information Networks · Computer Science 2025-12-25 Jeremie Fish , Mahesh Banavar , Erik Bollt

Dynamic connectivity is a well-studied problem, but so far the most compelling progress has been confined to the edge-update model: maintain an understanding of connectivity in an undirected graph, subject to edge insertions and deletions.…

Data Structures and Algorithms · Computer Science 2008-08-11 Timothy M. Chan , Mihai Patrascu , Liam Roditty

We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…

Probability · Mathematics 2023-09-19 Henry-Louis de Kergorlay , Desmond J. Higham

Centrality metrics have been widely applied to identify the nodes in a graph whose removal is effective in decomposing the graph into smaller sub-components. The node--removal process is generally used to test network robustness against…

Social and Information Networks · Computer Science 2022-04-25 Lucia Cavallaro , Stefania Costantini , Pasquale De Meo , Antonio Liotta , Giovanni Stilo

Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…

Data Structures and Algorithms · Computer Science 2024-12-25 Shyan Akmal

Dismantling criminal networks or containing epidemics or misinformation through node removal is a well-studied problem. To evaluate the effectiveness of such efforts, one must measure the strength of the network before and after node…

Social and Information Networks · Computer Science 2025-07-18 Kartikeya Kansal , Arunabha Sen

Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…

Social and Information Networks · Computer Science 2021-10-25 Tiago Simas , Rion Brattig Correia , Luis M. Rocha

As network research becomes more sophisticated, it is more common than ever for researchers to find themselves not studying a single network but needing to analyze sets of networks. An important task when working with sets of networks is…

Social and Information Networks · Computer Science 2019-07-26 James P. Bagrow , Erik M. Bollt

Research on the robustness of the Internet has gained critical importance in the last decades because more and more individuals, societies and firms rely on this global network infrastructure for communication, knowledge transfer, business…

Networking and Internet Architecture · Computer Science 2021-03-10 Milena Oehlers , Benjamin Fabian

Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…

Data Structures and Algorithms · Computer Science 2024-04-16 Dylan Hyatt-Denesik , Afrouz Jabal Ameli , Laura Sanita

The outage performance of wireless networks with unstructured network topologies is investigated. The network reliability perspective of graph theory is used to obtain the network outage polynomial of generalized wireless networks by…

Information Theory · Computer Science 2019-04-30 Semiha Tedik Basaran , Gunes Karabulut Kurt , Frank R. Kschischang

This paper considers dynamic networks where vertices and edges represent manifest signals and causal dependencies among the signals, respectively. We address the problem of how to determine if the dynamics of a network can be identified…

Optimization and Control · Mathematics 2021-05-10 Xiaodong Cheng , Shengling Shi , Ioannis Lestas , Paul M. J. Van den Hof

We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…

Probability · Mathematics 2020-06-02 Markus Heydenreich , Christian Hirsch