Related papers: Robustness of Regular Graphs Based on Natural Conn…
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…
We introduce the concept of natural connectivity as a robustness measure of complex networks. The natural connectivity has a clear physical meaning and a simple mathematical formulation. It characterizes the redundancy of alternative paths…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…
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…
In weighted graphs the shortest path between two nodes is often reached through an indirect path, out of all possible connections, leading to structural redundancies which play key roles in the dynamics and evolution of complex networks. We…
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…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
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…
Random intersection graphs have received much attention for nearly two decades, and currently have a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. In this paper, we…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Regular ring lattices (RRLs) are defined as peculiar undirected circulant graphs constructed from a cycle graph, wherein each node is connected to pairs of neighbors that are spaced progressively in terms of vertex degree. This kind of…
In this paper, we present some new results describing connections between the spectrum of a regular graph and its generalized connectivity, toughness, and the existence of spanning trees with bounded degree.
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,…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…