Showing papers on "Katz centrality published in 2007"

A measure of centrality based on network efficiency

Abstract: We introduce delta centralities, a new class of measures of structural centrality for networks. In particular, we focus on a measure in this class, the information centrality C I , which is based on the concept of efficient propagation of information over the network. C I is defined for both valued and non-valued graphs, and applies to groups as well as individuals. The measure is illustrated and compared with respect to the standard centrality measures by using a classic network data set. The statistical distribution of information centrality is investigated by considering large computer generated graphs and two networks from the real world.

Centrality Estimation in Large Networks

Abstract: Centrality indices are an essential concept in network analysis. For those based on shortest-path distances the computation is at least quadratic in the number of nodes, since it usually involves solving the single-source shortest-paths (SSSP) problem from every node. Therefore, exact computation is infeasible for many large networks of interest today. Centrality scores can be estimated, however, from a limited number of SSSP computations. We present results from an experimental study of the quality of such estimates under various selection strategies for the source vertices.

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.

How accurate and statistically robust are catalytic site predictions based on closeness centrality

Abstract: We examine the accuracy of enzyme catalytic residue predictions from a network representation of protein structure. In this model, amino acid α-carbons specify vertices within a graph and edges connect vertices that are proximal in structure. Closeness centrality, which has shown promise in previous investigations, is used to identify important positions within the network. Closeness centrality, a global measure of network centrality, is calculated as the reciprocal of the average distance between vertex i and all other vertices. We benchmark the approach against 283 structurally unique proteins within the Catalytic Site Atlas. Our results, which are inline with previous investigations of smaller datasets, indicate closeness centrality predictions are statistically significant. However, unlike previous approaches, we specifically focus on residues with the very best scores. Over the top five closeness centrality scores, we observe an average true to false positive rate ratio of 6.8 to 1. As demonstrated previously, adding a solvent accessibility filter significantly improves predictive power; the average ratio is increased to 15.3 to 1. We also demonstrate (for the first time) that filtering the predictions by residue identity improves the results even more than accessibility filtering. Here, we simply eliminate residues with physiochemical properties unlikely to be compatible with catalytic requirements from consideration. Residue identity filtering improves the average true to false positive rate ratio to 26.3 to 1. Combining the two filters together has little affect on the results. Calculated p-values for the three prediction schemes range from 2.7E-9 to less than 8.8E-134. Finally, the sensitivity of the predictions to structure choice and slight perturbations is examined. Our results resolutely confirm that closeness centrality is a viable prediction scheme whose predictions are statistically significant. Simple filtering schemes substantially improve the method's predicted power. Moreover, no clear effect on performance is observed when comparing ligated and unligated structures. Similarly, the CC prediction results are robust to slight structural perturbations from molecular dynamics simulation.

Betweenness Centrality Measure in Dynamic Networks

Abstract: In this paper we propose three methods of measuring betweenness of individuals in networks which are best modeled as graphs with explicit time ordering on their edges. The betweenness centrality index is one of the basic measure in the analysis of social networks, but most of the work done for measuring the betweenness index of individuals is based on the aggregate representation of the network. Many network problems are based on fundamental relationship involving time. We incorporate the time factor in the aggregate graph representation of social networks to create dynamic networks. We define and measure the betweenness in this dynamic framework. We compare the three betweenness with the standard betweenness measure for the same network. We show that by incorporating the exact times of interactions among individuals in a network, we can better study the betweenness of individuals in the underlying network.

Centrality measures and vulnerability of spatial networks

Abstract: Effective management of infrastructural networks in the case of a crisis requires a prior analysis of the vulnerability of spatial networks and identification of critical locations where an interdiction would cause most damage and disruption. This paper presents a preliminary study into how a graph theoretic structural analysis could be used for this purpose. Centrality measures are combined with a dual graph modelling approach in order to identify critical locations in a spatial network. The results of a case study on a street network of a small area in the city of Helsinki indicate that ‘betweenness’ is the most promising centrality measure for this purpose. Other measures and properties of graphs are under consideration for eventually developing a risk model not only for one but for a group of colocated spatial networks.

Fingerprinting networks: Correlations of local and global network properties

Abstract: In complex networks a common task is to identify the most important or “central” nodes There are several definitions, often called centrality measures, which often lead to different results Here, we introduce fingerprints of networks, which we define as correlation plots of local and global network properties We show that these fingerprints are suitable tools for characterizing networks beyond single-quantity distributions In particular, we study the correlations between four local and global measures, namely the degree, the shortest-path betweenness, the random-walk betweenness and the subgraph centrality on different random-network models like Erdős–Renyi, small-world and Barabasi–Albert as well as on different real networks like metabolic pathways, social collaborations and computer networks and compare those fingerprints to determine the quality of those basic models The correlation fingerprints are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world

Emergence of global network property based on multi-agent voting model

Abstract: Recent studies have shown that various models can explain the emergence of complex networks, such as scale-free and small-world networks. This paper presents a different model to generate complex networks using a multi-agent approach. Each node is considered as an agent. Based on voting by all agents, edges are added repeatedly. We use four different kinds of centrality measures as a utility functions for agents. Depending on the centrality measure, the resultant networks differ considerably: typically, closeness centrality generates a scale-free network, degree centrality produces a random graph, betweenness centrality favors a regular graph, and eigenvector centrality brings a complete subgraph. The importance of the network structure among agents is widely noted in the multi-agent research literature. This paper contributes new insights into the connection between agents' local behavior and the global property of the network structure. We describe a detailed analysis on why these structures emerge, and present a discussion of the possible expansion and application of the model.

Co-Betweenness: A Pairwise Notion of Centrality

Abstract: Betweenness centrality is a metric that seeks to quantify a sense of the importance of a vertex in a network graph in terms of its "control" on the distribution of information along geodesic paths throughout that network. This quantity however does not capture how different vertices participate together in such control. In order to allow for the uncovering of finer details in this regard, we introduce here an extension of betweenness centrality to pairs of vertices, which we term co-betweenness, that provides the basis for quantifying various analogous pairwise notions of importance and control. More specifically, we motivate and define a precise notion of co-betweenness, we present an efficient algorithm for its computation, extending the algorithm of Brandes in a natural manner, and we illustrate the utilization of this co-betweenness on a handful of different communication networks. From these real-world examples, we show that the co-betweenness allows one to identify certain vertices which are not the most central vertices but which, nevertheless, act as important actors in the relaying and dispatching of information in the network.

Dependence Centrality: Identifying Dependence of Nodes in Terrorist Networks

Abstract: Summary form only given. A new model of dependence centrality is proposed. The centrality measure is based on shortest paths between the pair of nodes. We apply this measure with demonstration of small network example. The comparisons are made with betweenness centrality. We discuss how investigative world / intelligence agencies could be benefited from the proposed measure.

Quasi-stationary distributions as centrality measures of reducible graphs

Abstract: Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was solved by introduction of uniform random jumps with some probability. Up to the present, there is no clear criterion for the choice this parameter. We propose to use parameter-free centrality measure which is based on the notion of quasi-stationary distribution. Specifically we suggest four quasi-stationary based centrality measures, analyze them and conclude that they produce approximately the same ranking. The new centrality measures can be applied in spam detection to detect ``link farms'' and in image search to find photo albums.