Related papers: Link Residual Closeness of Harary Graphs

Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the…

Link residual closeness is a newly proposed measure for network vulnerability. In this model, vertices are perfectly reliable and the links fail independently of each other. It measures the vulnerability even when the removal of links does…

Closeness is one of the most studied characteristics of networks. Residual closeness is a very sensitive measure of graphs robustness. Additional closeness is a measure of growth potentials of networks. In this article we calculate the…

Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…

The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper we provide an upper bound of the Harary index in terms of the vertex or edge connectivity of a graph. We…

Closeness is an important measure of network centrality. In this article we will calculate the closeness of graphs, created by using operations on graphs. We will prove a formula for the closeness of shadow graphs. We will calculate the…

We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…

Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the…

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…

The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of…

In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is…

Understanding the structures why links are formed is an important and prominent research topic. In this paper, we therefore consider the link prediction problem in face-to-face contact networks, and analyze the predictability of new and…

Link prediction is a key problem for network-structured data. Link prediction heuristics use some score functions, such as common neighbors and Katz index, to measure the likelihood of links. They have obtained wide practical uses due to…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

The problem of node-similarity in networks has motivated a plethora of such measures between node-pairs, which make use of the underlying graph structure. However, higher-order relations cannot be losslessly captured by mere graphs and…

This paper proposes a new graph proximity measure. This measure is a derivative of network reliability. By analyzing its properties and comparing it against other proximity measures through graph examples, we demonstrate that it is more…

Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…

Link Prediction is an important and well-studied problem for social networks. Given a snapshot of a graph, the link prediction problem predicts which new interactions between members are most likely to occur in the near future. As networks…

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 importance of studying properties of networks is manifest in diverse fields ranging from biology, engineering, physics, chemistry, neuroscience, and medicine. The functionality of networks with regard to performance, throughput,…