Related papers: Robustness of Regular Graphs Based on Natural Conn…

Interdependent networks have been shown to be extremely vulnerable based on the percolation model. Parshani et. al further indicated that the more inter-similar networks are, the more robust they are to random failure. Our understanding of…

How can the `affinity' or `strength' of ties of a random graph be characterized and compactly represented? How can concepts like Fourier and inverse-Fourier like transform be developed for graph data? To do so, we introduce a new…

In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the…

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…

With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper…

Predicting the occurrence of links is a fundamental problem in networks. In the link prediction problem we are given a snapshot of a network and would like to infer which interactions among existing members are likely to occur in the near…

Random key graphs form a class of random intersection graphs and are naturally induced by the random key predistribution scheme of Eschenauer and Gligor for securing wireless sensor network (WSN) communications. Random key graphs have…

We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…

Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance,…

I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…

We investigate simplified models of computer data networks and examine how the introduction of additional random links influences the performance of these net works. In general, the impact of additional random links on the performance of…

This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…

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.…

We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…

The robustness of a network is depending on the type of attack we are considering. In this paper we focus on the spread of viruses on networks. It is common practice to use the epidemic threshold as a measure for robustness. Because the…

The average effective resistance of a graph is a relevant performance index in many applications, including distributed estimation and control of network systems. In this paper, we study how the average resistance depends on the graph…

To describe the flow of a miscible quantity on a network, we introduce the graph wave equation where the standard continuous Laplacian is replaced by the graph Laplacian. This is a natural description of an array of inductances and…

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…

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its…