Showing papers on "Katz centrality published in 2006"

Centrality in networks of urban streets

Abstract: Centrality has revealed crucial for understanding the structural properties of complex relational networks. Centrality is also relevant for various spatial factors affecting human life and behaviors in cities. Here, we present a comprehensive study of centrality distributions over geographic networks of urban streets. Five different measures of centrality, namely degree, closeness, betweenness, straightness and information, are compared over 18 1-square-mile samples of different world cities. Samples are represented by primal geographic graphs, i.e., valued graphs defined by metric rather than topologic distance where intersections are turned into nodes and streets into edges. The spatial behavior of centrality indices over the networks is investigated graphically by means of color-coded maps. The results indicate that a spatial analysis, that we term multiple centrality assessment, grounded not on a single but on a set of different centrality indices, allows an extended comprehension of the city structure, nicely capturing the skeleton of most central routes and subareas that so much impacts on spatial cognition and on collective dynamical behaviors. Statistically, closeness, straightness and betweenness turn out to follow similar functional distribution in all cases, despite the extreme diversity of the considered cities. Conversely, information is found to be exponential in planned cities and to follow a power-law scaling in self-organized cities. Hierarchical clustering analysis, based either on the Gini coefficients of the centrality distributions, or on the correlation between different centrality measures, is able to characterize classes of cities.

Using structure indices for efficient approximation of network properties

Abstract: Statistics on networks have become vital to the study of relational data drawn from areas such as bibliometrics, fraud detection, bioinformatics, and the Internet. Calculating many of the most important measures - such as betweenness centrality, closeness centrality, and graph diameter-requires identifying short paths in these networks. However, finding these short paths can be intractable for even moderate-size networks. We introduce the concept of a network structure index (NSI), a composition of (1) a set of annotations on every node in the network and (2) a function that uses the annotations to estimate graph distance between pairs of nodes. We present several varieties of NSIs, examine their time and space complexity, and analyze their performance on synthetic and real data sets. We show that creating an NSI for a given network enables extremely efficient and accurate estimation of a wide variety of network statistics on that network.

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.

Correlations among centrality measures in complex networks

Abstract: In this paper, we empirically investigate correlations among four centrality measures, originated from the social science, of various complex networks. For each network, we compute the centrality measures, from which the partial correlation as well as the correlation coefficient among measures is estimated. We uncover that the degree and the betweenness centrality are highly correlated; furthermore, the betweenness follows a power-law distribution irrespective of the type of networks. This characteristic is further examined in terms of the conditional probability distribution of the betweenness, given the degree. The conditional distribution also exhibits a power-law behavior independent of the degree which explains partially, if not whole, the origin of the power-law distribution of the betweenness. A similar analysis on the random network reveals that these characteristics are not found in the random network.

Practical algorithms for destabilizing terrorist networks

Abstract: This paper uses centrality measures from complex networks to discuss how to destabilize terrorist networks. We propose newly introduced algorithms for constructing hierarchy of covert networks, so that investigators can view the structure of terrorist networks / non-hierarchical organizations, in order to destabilize the adversaries. Based upon the degree centrality, eigenvector centrality, and dependence centrality measures, a method is proposed to construct the hierarchical structure of complex networks. It is tested on the September 11, 2001 terrorist network constructed by Valdis Krebs. In addition we also propose two new centrality measures i.e., position role index (which discovers various positions in the network, for example, leaders / gatekeepers and followers) and dependence centrality (which determines who is depending on whom in a network). The dependence centrality has a number of advantages including that this measure can assist law enforcement agencies in capturing / eradicating of node (terrorist) which may disrupt the maximum of the network.

Practical algorithms for destabilizing terrorist networks

Abstract: This paper uses centrality measures from complex networks to discuss how to destabilize terrorist networks. We propose newly introduced algorithms for constructing hierarchy of covert networks, so that investigators can view the structure of terrorist networks / non-hierarchical organizations, in order to destabilize the adversaries. Based upon the degree centrality, eigenvector centrality, and dependence centrality measures, a method is proposed to construct the hierarchical structure of complex networks. It is tested on the September 11, 2001 terrorist network constructed by Valdis Krebs. In addition we also propose two new centrality measures i.e., position role index (which discovers various positions in the network, for example, leaders / gatekeepers and followers) and dependence centrality (which determines who is depending on whom in a network). The dependence centrality has a number of advantages including that this measure can assist law enforcement agencies in capturing / eradicating of node (terrorist) which may disrupt the maximum of the network.

Use and Methods of Social Network Analysis in Knowledge Management

Abstract: Whilst the primary importance of informal communities of practice and knowledge networks in innovation and knowledge management is widely accepted (see Armbrecht et al., 2001; Brown & Duguid, 1991; Collinson & Gregson, 2003; Jain & Triandis, 1990; Lesser, 2001; Liyanage, Greenfied & Don, 1999; Nahapiet & Ghoshal, 1998; Nohria & Eccles, 1992; Wenger, 1999; Zanfei, 2000), there is less agreement on the most appropriate method for their empirical study and theoretical analysis. In this article it is argued that social network analysis (SNA) is a highly effective tool for the analysis of knowledge networks, as well as for the identification and implementation of practical methods in knowledge management and innovation. Social network analysis is a sociological method to undertake empirical analysis of the structural patterns of social relationships in networks (see, e.g., Scott, 1991; Wasserman & Faust, 1994; Wellman & Berkowitz, 1988). This article aims at demonstrating how it can be used to identify, visualize, and analyze the informal personal networks that exist within and between organizations according to structure, content, and context of knowledge flows. It will explore the benefits of social network analysis as a strategic tool on the example of expert localization and knowledge transfer, and also point to the limits of the method.

Discovering Hierarchical Structure in Terrorist Networks

Abstract: The network structure of a group determines its strengths and weaknesses. A general knowledge of the prevalent models of terrorist organizations and its analysis methods leads to a better understanding of their capabilities. One important method is centrality analysis, which determines the relative importance of vertices (terrorists) in a network based on their connectivity within the network structure. In this paper, we address the hierarchy property sharing among a large amount of networks. Based upon the degree centrality (DC) and eigenvector centrality (EC) measure, a method is proposed to discover the hierarchical structure of a terrorist network. This hierarchical structure sheds light on the leadership and the likely sub groups embedded in the network