Network theory

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

Visual analysis of network centralities

Abstract: Centrality analysis determines the importance of vertices in a network based on their connectivity within the network structure. It is a widely used technique to analyse network-structured data. A particularly important task is the comparison of different centrality measures within one network. We present three methods for the exploration and comparison of centrality measures within a network: 3D parallel coordinates orbit-based comparison and hierarchy-based comparison. There is a common underlying idea to all three methods: for each centrality measure the graph is copied and drawn in a separate 2D plane with vertex position dependent on centrality. These planes are then stacked into the third dimension so that the different centrality measures may be easily compared. Only the details of how centrality is mapped to vertex position are dierent in each method. For 3D parallel coordinates vertices are placed on vertical lines; for orbit-based comparison vertices are placed on concentric circles and for hierarchy-based comparison vertices are placed on horizontal lines. The second and third solutions make it particularly easy to track changing vertex-centrality values in the context of the underlying network structure. The usability of these methods is demonstrated on biological and social networks.

An algorithm for k-degree anonymity on large networks

Abstract: In this paper, we consider the problem of anonymization on large networks. There are some anonymization methods for networks, but most of them can not be applied on large networks because of their complexity. We present an algorithm for k-degree anonymity on large networks. Given a network G, we construct a k-degree anonymous network, G, by the minimum number of edge modifications. We devise a simple and efficient algorithm for solving this problem on large networks. Our algorithm uses univariate micro-aggregation to anonymize the degree sequence, and then it modifies the graph structure to meet the k-degree anonymous sequence. We apply our algorithm to a different large real datasets and demonstrate their efficiency and practical utility.

The Web of Law

Abstract: Scientists and mathematicians in recent years have become intensely interested in the structure of networks. Networks turn out to be crucial to understanding everything from physics and biology, to economics and sociology. This article proposes that the science of networks has important contributions to make to the study of law as well. The network of American case law closely resembles the Web in structure and can be studied using techniques that are now being used to describe many other networks, some found in nature, and others created by human action. Studying the legal network can shed light on how the legal system evolves, and many other questions. I present in this article the preliminary results of a significant citation study of nearly four million American legal precedents, which was undertaken at my request by the LexisNexis corporation using the Shepard's citation service. This study demonstrates that the American case law network has the overall structure that network theory predicts it would. It is a highly skewed, scale-free, or similar network. The remarkably great degree of skew is significant. Precendential authority is concentrated in a small number of cases. The vast majority of cases are rarely or never cited. In that it consists largely of dead cases, the Web of Law closely resembles scientific paper citation networks, which consist mostly of dead papers. This article has three parts. First, I introduce some basic concepts of network science, including such important ideas as nodes, links, random graphs, evolving networks, scale-free networks, small worlds, the rich get richer dynamic, node fitness, and clusters. In Part II, I show that both over all and by particular jurisdiction, the Web of Law is a scale-free or similarly highly skewed network. In Part III, I describe some insights that appear from this application and suggest areas for future research. The Web of Law has a structure very similar to that of other real networks, such as the Web and the network of scientific papers. Indeed, preliminary analysis suggests the citation network of U.S. Supreme Court cases is nearly identical to the network of high-energy physics papers, and is well described by a two-power-law model. The Web of Law is organized with hub cases that have many citations and the vast majority of cases, which have very few. The distribution of citation frequency appears to be well described by a two power-law distribution, very similar to scientific paper citation networks. Many promising hypotheses can be generated by considering the law as a scale-free network. State and federal systems can be examined empirically to measure how well integrated each is with itself, and with each other, and how this is changing over time. Legal authorities can be measured to determine whether their authority is emerging or declining. Institutional bodies, such as courts, can be examined in the same way. Clusters of cases, which will reveal the semantic topology of law, can be mapped to determine whether traditional legal categories are accurate or require reform. These methods can be used to develop computer programs to improve the efficiency of searching electronic legal databases. Network theory hints at complex, but analyzable, interactions between the legal doctrines of precedent, and the systems of common law and multiple sovereignties. Because law grows and because it has doctrines of authority, it creates a network of a certain shape, which spontaneously organizes itself. Legal databases, which are huge, precisely documented, and readily accessible, present a perfect opportunity for the application of network science. This research would produce new knowledge of general jurisprudence that has simply been impossible until now, when we have the necessary advances in network science, the fast computers, and the existence of a complete record of the legal network in electronic form, waiting to be explored.

A biplex approach to PageRank centrality: From classic to multiplex networks.

Abstract: In this paper, we present a new view of the PageRank algorithm inspired by multiplex networks. This new approach allows to introduce a new centrality measure for classic complex networks and a new proposal to extend the usual PageRank algorithm to multiplex networks. We give some analytical relations between these new approaches and the classic PageRank centrality measure, and we illustrate the new parameters presented by computing them on real underground networks.

Death of Distance in Science? A Gravity Approach to Research Collaboration

Abstract: One of the major transitions in recent scientific research is the rise of network theory motivating a variety∈dexvariety of new research programmes in and across various disciplines. Economic geography∈dexgeography has been no exception. The work on networks in economic geography can be divided into two types of research. First, there are studies on inter-firm networks and their impact on firm performance. For a large part, such studies have been carried out in the context of geographical clusters, which are often characterised by strong network relations (Uzzi, 1997). A second approach, an example of which is presented below, concerns the study of inter-regional networks and their impact on regional growth. Here, the unit of analysis are territories, typically sub-national regions. The interest in this topic stems from Castells (1996) and others who have argued that regional growth increasingly depends on a region’s position in global networks rather than its specific local characteristics such as institutions, endowments and amenities (‘space of flows’ versus the ‘space of places’).