Showing papers on "Katz centrality published in 2010"

A New Measure of Centrality for Brain Networks

Abstract: Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centrality being three of the most popular measures. Degree identifies the most connected nodes, whereas betweenness centrality identifies those located on the most traveled paths. Eigenvector centrality considers nodes connected to other high degree nodes as highly central. In the work presented here, we propose a new centrality metric called leverage centrality that considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its immediate neighbors rely on that node for information. Although similar in concept, there are essential differences between eigenvector and leverage centrality that are discussed in this manuscript. Degree, betweenness, eigenvector, and leverage centrality were compared using functional brain networks generated from healthy volunteers. Functional cartography was also used to identify neighborhood hubs (nodes with high degree within a network neighborhood). Provincial hubs provide structure within the local community, and connector hubs mediate connections between multiple communities. Leverage proved to yield information that was not captured by degree, betweenness, or eigenvector centrality and was more accurate at identifying neighborhood hubs. We propose that this metric may be able to identify critical nodes that are highly influential within the network.

Centrality metric for dynamic networks

Abstract: Centrality is an important notion in network analysis and is used to measure the degree to which network structure contributes to the importance of a node in a network. While many different centrality measures exist, most of them apply to static networks. Most networks, on the other hand, are dynamic in nature, evolving over time through the addition or deletion of nodes and edges. A popular approach to analyzing such networks represents them by a static network that aggregates all edges observed over some time period. This approach, however, under or overestimates centrality of some nodes. We address this problem by introducing a novel centrality metric for dynamic network analysis. This metric exploits an intuition that in order for one node in a dynamic network to influence another over some period of time, there must exist a path that connects the source and destination nodes through intermediaries at different times. We demonstrate on an example network that the proposed metric leads to a very different ranking than analysis of an equivalent static network. We use dynamic centrality to study a dynamic citations network and contrast results to those reached by static network analysis.

Centrality scaling in large networks.

Abstract: Betweenness centrality lies at the core of both transport and structural vulnerability properties of complex networks; however, it is computationally costly, and its measurement for networks with millions of nodes is nearly impossible. By introducing a multiscale decomposition of shortest paths, we show that the contributions to betweenness coming from geodesics not longer than L obey a characteristic scaling versus L, which can be used to predict the distribution of the full centralities. The method is also illustrated on a real-world social network of 5.5 × 10(6) nodes and 2.7 × 10(7) links.

Topological centrality and its e-Science applications

Abstract: Network structure analysis plays an important role in characterizing complex systems. Different from previous network centrality measures, this article proposes the topological centrality measure reflecting the topological positions of nodes and edges as well as influence between nodes and edges in general network. Experiments on different networks show distinguished features of the topological centrality by comparing with the degree centrality, closeness centrality, betweenness centrality, information centrality, and PageRank. The topological centrality measure is then applied to discover communities and to construct the backbone network. Its characteristics and significance is further shown in e-Science applications. © 2010 Wiley Periodicals, Inc.

Centrality measure in graphs

Abstract: Centrality of an edge of a graph is proposed to be viewed as a degree of global sensitivity of a graph distance function (i.e., a graph metric) on the weight of the considered edge. For different choices of distance function, contact is made with several previous ideas of centrality, whence their different characteristics are clarified, and strengths or short-comings are indicated, via selected examples. The centrality based on “resistance distance” exhibits several nice features, and might be termed “amongness” centrality.

A vibrational approach to node centrality and vulnerability in complex networks

Abstract: We propose a new measure of vulnerability of a node in a complex network. The measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs. We define the measure as the node displacement, or the amplitude of vibration of each node, under fluctuation due to the thermal bath in which the network is supposed to be submerged. We prove exact relations among the thus defined node displacement, the information centrality and the Kirchhoff index. The relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality, because the latter is the sum of the local node displacement and the node displacement averaged over the entire network.

Vertex centrality as a measure of information flow in Italian Corporate Board Networks

Abstract: The aim of this article is to investigate the governance models of companies listed on the Italian Stock Exchange by using a network approach, which describes the interlinks between boards of directors. Following mainstream literature, I construct a weighted graph representing the listed companies (vertices) and their relationships (weighted edges), the Corporate Board Network; I then apply three different vertex centrality measures: degree, betweenness and flow betweenness. What emerges from the network construction and by applying the degree centrality is a structure with a large number of connections but not particularly dense, where the presence of a small number of highly connected nodes (hubs) is evident. Then I focus on betweenness and flow betweenness; indeed I expect that these centrality measures may give a representation of the intensity of the relationship between companies, capturing the volume of information flowing from one vertex to another. Finally, I investigate the possible scale-free structure of the network.

Resistance Distance, Information Centrality, Node Vulnerability and Vibrations in Complex Networks

Abstract: We discuss three seemingly unrelated quantities that have been intro- duced in different fields of science for complex networks. The three quantities are the resistance distance, the information centrality and the node displacement. We first prove various relations among them. Then we focus on the node displacement, showing its usefulness as an index of node vulnerability. We argue that the node dis- placement has a better resolution as a measure of node vulnerability than the degree and the information centrality.

A KLT-inspired node centrality for identifying influential neighborhoods in graphs

Abstract: We present principal component centrality (PCC) as a measure of centrality that is more general and encompasses eigenvector centrality (EVC). We explain some of the difficulties in applying EVC to graphs and networks that contain more than just one neighborhood of nodes with high influence. We demonstrate the shortcomings of traditional EVC and contrast it against PCC. PCC's ranking procedure is based on spectral analysis of the network's graph adjacency matrix and identification of its most significant eigenvectors.

Dynamics-based centrality for directed networks.

Abstract: Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.

Zonal centrality measures and the neighborhood effect

Abstract: The goal of this study is to develop a robust methodology for computing zone centrality measures in an urban area. Centrality refers to the relative importance of a zone in terms of network efficiency and utility for both transportation and urban study. Centrality indices that were developed to describe human relationships in the field of structural sociology were adopted. It is important to accommodate the neighborhood effect in dealing with centrality. The neighborhood effect describes the phenomenon whereby the attractiveness of a specific zone is affected by its neighbor zones. Kernel functions were employed to accommodate the neighborhood effect. The optimal bandwidth parameters were derived indirectly within the framework of trip attraction estimation under the assumption that the trip attraction of a zone is influenced by the integrated centrality, which includes the neighborhood effect. The well-known estimation tool of maximum likelihood estimation (MLE) was adopted to find the optimal bandwidth. As a byproduct of accommodating the neighborhood effect in centralities, a considerable advantage of the present study is an enhancement of the performance of trip attraction model. Another meaningful contribution of this study is a solution to the question of an acceptable delineation of the two city centers in Seoul. The boundaries of the two city centers were derived based on both the kernel function and its bandwidth.

Centrality in Directed Social Networks: A Game Theoretic Approach

Abstract: In this paper we define a family of centrality measures for directed social networks from a game theoretical point of view. We follow the line started with our previous work (Gomez et al.., 2003). Besides the definition, we obtain both, a characterization and an additive decomposition of the measures.

Probabilistic Paths and Centrality in Time

Abstract: Traditionally, graph centrality measures such as betweenness centrality are applied to discrete, static graphs, where binary edges represent the ‘presence’ or ‘absence’ of a relationship. However, when considering the evolution of networks over time, it is more natural to consider interactions at particular timesteps as observational evidence of the latent (i.e., hidden) relationships among entities. In this formulation, there is inherent uncertainty about the strength of the underlying relationships and/or whether they are still active at a particular point in time. For example, if we observe an email communication between two people at time t, that indicates they have an active relationship at t, but at time t + k we are less certain the relationship still holds. In this work, we develop a framework to capture this uncertainty, centered around the notion of probabilistic paths. In order to model the effect of relationship uncertainty on network connectivity and its change over time, we formulate a measure of centrality based on most probable paths of communication, rather than shortest paths. In addition to the notion of the relationship strength, we also incorporate uncertainty with regard to the transmission of information using a binomial prior. We show that shortest paths in a unweighted, discrete graph can be formulated using probabilistic paths with a prior and we develop an algorithm to compute the most likely paths in O ` |V ||E| + |V | 2 log |V | ´ . We demonstrate the effectiveness of our approach by computing probabilistic betweenness centrality over time in the the Enron email dataset.

Information Diffusion and δ-Closeness-Centrality

Abstract: I consider the issue of optimal targeting in information diffusion networks. The initial information possessor is to target a single node so as to disseminate the infor-mation to all other nodes most effectively. For the purpose, the concept of closeness centrality may be useful, but if the value from delayed information is discounted by a discount factor, the concept should be properly modified. With this respect, I propose a modified concept of point centrality which I will call δ-(closeness)-centrality. The δ-centrality of a node is defined by the sum of discounted values generated from infor-mation transmission starting from the node given discount factor δ. I also provide some alternative scenarios that could justify various measures of closeness-based centrality.

Two-Dimensional Centrality of Asymmetric Social Network

Abstract: The purpose of the present study is to introduce a procedure to derive the centrality of an asymmetric social network, where the relationships among actors are asymmetric. The procedure is based on the singular value decomposition of an asymmetric matrix of friendship relationships among actors. Two kinds of the centrality are introduced; one is the centrality of extending friendship relationships from the actor to the other actors, and the other is the centrality of accepting friendship relationships from the other actors to the actor. The present procedure is based on the two largest singular values not only on the largest singular value. Each actor has two sets of the centrality; each consists of the centrality of extending and of the centrality of accepting friendship relationships. An application to help or advice relationships among managers in a company is shown.

Network Analysis on Centrality of Airport System

Abstract: The airport system is an important component for the organization of aviation transportation. It is an effective way to analyze the constitution of air transportation and urban systems by identifying the spatial structure of airport system. Centrality is one of the basic methods. Based on network analysis, three common indices, degree centrality, closeness centrality and betweenness centrality were used to measure centrality for individual cities in the paper. That is to say, "Being central" is not limited to being connected to others, but also being close to all others and being intermediary between others. In the airport system of China, degree centrality shows the "Ding Pattern" for the top class and the "Flyover Effect" for the national network. Closeness centrality makes it measurable for the airport service. Betweenness centrality is a good measure to analyze regional hubs and the core-periphery pattern. On individual cities, Beijing and Shanghai are clearly the top two central cities in all three indices; and rankings on other cities by the betweenness centrality differ significantly from those by the degree and closeness centralities. Based on the three centrality indices, an Exploratory Weighted Method (EWM) were put forward, namely system centrality, to do a further research. The results showed the hierarchical structure with the "Ding Pattern" in the top class and the "Flyover Effect" in the national network. Besides, the spatial pattern by the system centrality accords well with the five airport clusters designed in the National Civil Airports Deployment Plan.

Hirsch index as a network centrality measure

Abstract: We study the h Hirsch index as a local node centrality measure for complex networks in general. The h index is compared with the Degree centrality (a local measure), the Betweenness and Eigenvector centralities (two non-local measures) in the case of a biological network (Yeast interaction protein-protein network) and a linguistic network (Moby Thesaurus II) as test environments. In both networks, the Hirsch index has poor correlation with Betweenness centrality but correlates well with Eigenvector centrality, specially for the more important nodes that are relevant for ranking purposes, say in Search Machine Optimization. In the thesaurus network, the h index seems even to outperform the Eigenvector centrality measure as evaluated by simple linguistic criteria.

A centrality measure based on spectral optimization of modularity density

Abstract: Centrality analysis has been shown to be a valuable method for the structural analysis of complex networks. It is used to identify key elements within networks and to rank network elements such that experiments can be tailored to interesting candidates. In this paper, we show that the optimization process of modularity density can be written in terms of the eigenspectrum of kernel matrix. Based on the eigenvectors belonging to the largest eigenvalue of kernel matrix, we present a new centrality measure that characterizes the contribution of each node to its assigned community in a network, called modularity density centrality. The measure is illustrated and compared with the standard centrality measures by using respectively an artificial example and a classic network data set. The statistical distribution of modularity density centrality is investigated by considering large computer generated graphs and two large networks from the real world. Experimental results show the significance of the proposed approach.

Modularity matrix of networks and the measure of community structure

Abstract: The relationships between positive （negative） eigenspectrums and the structure properties of community （anti-community） of complex networks are investigated, and some corresponding definitions are given. By using the multieigenspectrums of modularity matrix of networks, a kind of structural centrality measure called the community centrality, is introduced. This individual centrality measure describes the strength that the individual adheres to the corresponding community. The measure is illustrated and compared with the standard centrality measures using several artificial networks and real world networks data. The results show that the community centrality has better discrimination, and it has positive correlation with the degree centrality.

CENTPOW: Stata module to calculate centrality and power indices for each node in a network.

Abstract: module to calculate degree centrality, alter-based centrality and power, and beta centrality and power for each node in a symmetric network.

Betweenness Centrality Analysis for Urban Road Networks

Abstract: The spatial distribution of road networks is a fundamental issue in spatial analysis of GIS for Transportation.Betweenness Centrality is extensively used to evaluate the importance of nodes for the analysis of complicated networks.In this paper,six typical urban road networks were selected and transformed to direct graphs for the analysis of betweenness centrality.The results show that the distribution of betweenness centrality shows consistency and has a hierarchical property.The statistical results of betweenness centrality illustrates that the majority of road segments in high administrative levels characterize high value while the majority of road segments in low administrative levels have low value in urban road networks.The experimental results show that there is a correlation between the Betweenness Centrality hierarchy in mathematical measure and the administrative levels.