Related papers: Hierarchy depth in directed networks
In physics, biology and engineering, network systems abound. How does the connectivity of a network system combine with the behavior of its individual components to determine its collective function? We approach this question for networks…
We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
This paper presents an analytical framework to model fault-tolerance in unstructured peer-to-peer overlays, represented as complex networks. We define a distributed protocol peers execute for managing the overlay and reacting to node…
Network measurement probes the underlying network to support upper-level decisions such as network management, network update, network maintenance, network defense and beyond. Due to the massive, speedy, unpredictable features of network…
This paper proposes a new class of assortativity measures for weighted and directed networks. We extend the classical Newman's degree-degree assortativity by considering nodes' attributes different from the degree. Moreover, we propose…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with…
We define gradient networks as directed graphs formed by local gradients of a scalar field distributed on the nodes of a substrate network G. We derive an exact expression for the in-degree distribution of the gradient network when the…
We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-R\'enyi networks, based on recursion equations for the shells around a reference node and for the paths originating from…
A network's assortativity is the tendency of vertices to bond with others based on similarities, usually excess vertex degree. In this paper we consider assortativity in weighted networks, both directed and undirected. To this end, we…
We consider the number of paths that must pass through a subset $X$ of vertices of a network $N$ in a maximum sequence of arc-disjoint paths connecting two vertices $y$ and $z$. We show that when $X$ is a singleton, that number equals the…
Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In…
Different types of graphs and complex networks have been characterized, analyzed, and modeled based on measurements of their respective topology. However, the available networks may constitute approximations of the original structure as a…
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 a recent paper, Kwon and Oum claim that every graph of bounded rank-width is a pivot-minor of a graph of bounded tree-width (while the converse has been known true already before). We study the analogous questions for "depth" parameters…
We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models.…
Only when understanding hackers' tactics, can we thwart their attacks. With this spirit, this paper studies how hackers can effectively launch the so-called 'targeted node attacks', in which iterative attacks are staged on a network, and in…
A geometric entropy is defined as the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability…
The arrangement of network nodes in hyperbolic spaces has become a widely studied problem, motivated by numerous results suggesting the existence of hidden metric spaces behind the structure of complex networks. Although several methods…