Network theory

About: Network theory is a research topic. Over the lifetime, 2257 publications have been published within this topic receiving 109864 citations.

Fast algorithm for successive computation of group betweenness centrality.

Abstract: In this paper, we propose a method for rapid computation of group betweenness centrality whose running time (after preprocessing) does not depend on network size. The calculation of group betweenness centrality is computationally demanding and, therefore, it is not suitable for applications that compute the centrality of many groups in order to identify new properties. Our method is based on the concept of path betweenness centrality defined in this paper. We demonstrate how the method can be used to find the most prominent group. Then, we apply the method for epidemic control in communication networks. We also show how the method can be used to evaluate distributions of group betweenness centrality and its correlation with group degree. The method may assist in finding further properties of complex networks and may open a wide range of research opportunities.

Networks: A Very Short Introduction

Abstract: From ecosystems to Facebook, from the Internet to the global financial market, some of the most important and familiar natural systems and social phenomena are based on a networked structure. It is impossible to understand the spread of an epidemic, a computer virus, large-scale blackouts, or massive extinctions without taking into account the network structure that underlies all these phenomena. In this Very Short Introduction, Guido Caldarelli and Michele Catanzaro discuss the nature and variety of networks, using everyday examples from society, technology, nature, and history to explain and understand the science of network theory. They show the ubiquitous role of networks; how networks self-organize; why the rich get richer; and how networks can spontaneously collapse. They conclude by highlighting how the findings of complex network theory have very wide and important applications in genetics, ecology, communications, economics, and sociology.

Visual Reasoning about Social Networks Using Centrality Sensitivity

Abstract: In this paper, we study the sensitivity of centrality metrics as a key metric of social networks to support visual reasoning. As centrality represents the prestige or importance of a node in a network, its sensitivity represents the importance of the relationship between this and all other nodes in the network. We have derived an analytical solution that extracts the sensitivity as the derivative of centrality with respect to degree for two centrality metrics based on feedback and random walks. We show that these sensitivities are good indicators of the distribution of centrality in the network, and how changes are expected to be propagated if we introduce changes to the network. These metrics also help us simplify a complex network in a way that retains the main structural properties and that results in trustworthy, readable diagrams. Sensitivity is also a key concept for uncertainty analysis of social networks, and we show how our approach may help analysts gain insight on the robustness of key network metrics. Through a number of examples, we illustrate the need for measuring sensitivity, and the impact it has on the visualization of and interaction with social and other scale-free networks.

Using mapping entropy to identify node centrality in complex networks

Abstract: The problem of finding the best strategy to attack a network or immunize a population with a minimal number of nodes has attracted much current research interest. The assessment of node importance has been a fundamental issue in the research of complex networks. In this paper, we propose a new concept called mapping entropy (ME) to identify the importance of a node in the complex network. The concept is established according to the local information which considers the correlation among all neighbors of a node. We evaluate the efficiency of the centrality by static and dynamic attacks on standard network models and real-world networks. The simulation result shows that the new centrality is more efficient than traditional attack strategies, whether it is static or dynamic.