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Showing papers on "Katz centrality published in 2011"


Journal ArticleDOI
TL;DR: In this paper, the authors examined the network structure and nodal centrality of individual cities in the air transport network of China (ATNC) using a complex network approach and found that the ATNC has a cumulative degree distribution captured by an exponential function, and displays some small-world network properties with an average path length of 2.23 and a clustering coefficient of 0.69.

398 citations


Journal ArticleDOI
TL;DR: A theoretical model based on social network theories and analytical methods for exploring collaboration (co-authorship) networks of scholars suggests that the professional social network of researchers can be used to predict the future performance of researchers.

380 citations


Proceedings ArticleDOI
04 Jan 2011
TL;DR: A theoretical model based on social network theory shows that scholars, who maintain a strong co-authorship relationship to only one co-author of a group of linked co-authors, perform better than those researchers with many relationships to the same group of links.
Abstract: In this study, we develop a theoretical model based on social network theory to understand how the collaboration (co-authorship) network of scholars correlates to the research performance of scholars. For this analysis, we use social network analysis (SNA) measures (i.e., normalized closeness centrality, normalized betweenness centrality, efficiency, and two types of degree centrality). The analysis of data shows that the research performance of scholars is positively correlated with two SNA measures (i.e., weighted degree centrality and efficiency). In particular, scholars with strong ties (i.e., repeated co-authorships, i.e., high weighted degree centrality) show a better research performance than those with low ties (e.g., single co-authorships with many different scholars). The results related to efficiency show that scholars, who maintain a strong co-authorship relationship to only one co-author of a group of linked co-authors (i.e., co-authors that have joined publications), perform better than those researchers with many relationships to the same group of linked co-authors.

118 citations


Journal ArticleDOI
TL;DR: A novel form of centrality is introduced: the second order centrality which can be computed in a distributed manner which provides locally each node with a value reflecting its relative criticity and relies on a random walk visiting the network in an unbiased fashion.

89 citations


Proceedings ArticleDOI
05 Jun 2011
TL;DR: This paper identifies social hubs, nodes at the center of influential neighborhoods, in massive online social networks using principal component centrality (PCC), and compares PCC with eigenvector centrality's (EVC), the de facto measure of node influence by virtue of their position in a network.
Abstract: Identifying the most influential nodes in social networks is a key problem in social network analysis. However, without a strict definition of centrality the notion of what constitutes a central node in a network changes with application and the type of commodity flowing through a network. In this paper we identify social hubs, nodes at the center of influential neighborhoods, in massive online social networks using principal component centrality (PCC). We compare PCC with eigenvector centrality's (EVC), the de facto measure of node influence by virtue of their position in a network. We demonstrate PCC's performance by processing a friendship graph of 70, 000 users of Google's Orkut social networking service and a gaming graph of 143, 020 users obtained from users of Facebook's 'Fighters Club' application.

77 citations


Book ChapterDOI
27 Jun 2011
TL;DR: A centrality measure for independent cascade model, which is based on diffusion probability (or propagation probability) anddegree centrality and degree centrality is proposed, which indicates, k nodes obtained through (i) significantly outperform those obtain by (ii) and (iii).
Abstract: The paper addresses the problem of finding top k influential nodes in large scale directed social networks. We propose a centrality measure for independent cascade model, which is based on diffusion probability (or propagation probability) and degree centrality. We use (i) centrality based heuristics with the proposed centrality measure to get k influential individuals. We have also found the same using (ii) high degree heuristics and (iii) degree discount heuristics. A Monte-Carlo simulation has been conducted with top k-nodes found through different methods. The result of simulation indicates, k nodes obtained through (i) significantly outperform those obtain by (ii) and (iii). We further verify the differences statistically using T-Test and found the minimum significance level (p-value) when k > 5 is 0.022 compare with (ii) and 0.015 when comparing with (iii) for twitter data.

69 citations


Proceedings ArticleDOI
10 Apr 2011
TL;DR: Experimental evaluations on diverse real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared to known randomized algorithms.
Abstract: This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. Experimental evaluations on diverse real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared to known randomized algorithms.

65 citations


Journal ArticleDOI
TL;DR: A family of centrality measures for directed social networks from a game theoretical point of view is defined and a characterization of the measures and an additive decomposition in three summands that can be interpreted in terms of emission, betweenness and reception centrality components.

52 citations


Journal ArticleDOI
TL;DR: A discontinuous transition in the network density between hierarchical and homogeneous networks is found, depending on the rate of link decay, and this evolution mechanism leads to double power-law degree distributions, with interrelated exponents.
Abstract: We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arise under various centrality measures, and solve analytically the network evolution. During the complete evolution, the network is characterized by nestedness: the neighborhood of a node is contained in the neighborhood of the nodes with larger degree. We find a discontinuous transition in the network density between hierarchical and homogeneous networks, depending on the rate of link decay. We also show that this evolution mechanism leads to double power-law degree distributions, with interrelated exponents.

50 citations


Book ChapterDOI
30 May 2011
TL;DR: The relation-algebraic approach to the concepts of power and influence in social networks is presented, and some applications of relation algebra and RelView to this model are discussed.
Abstract: We deliver a short overview of different centrality measures and influence concepts in socialnetworks, and present the relation-algebraic approach to the concepts of power and influence. First, we briefly discuss four kinds of measures of centrality: the ones based on degree, closeness, betweenness, and the eigenvector-relatedmeasures.We consider centrality of a node and of a network.Moreover, we give a classification of the centrality measures based on a topology of network flows. Furthermore, we present a certainmodel of influence in a social network and discuss some applications of relation algebra and RelView to this model.

39 citations


Posted Content
TL;DR: In this paper, the authors develop measures of path length, betweenness centrality, and clustering coefficient based on probabilistic paths and evaluate them on three realworld networks from Enron, Facebook, and DBLP.
Abstract: Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a discrete link structure, complex systems must be transformed to this representation in order to investigate network properties. However, in many domains there may be uncertainty about the relationship structure and any uncertainty information would be lost in translation to a discrete representation. Uncertainty may arise in domains where there is moderating link information that cannot be easily observed, i.e., links become inactive over time but may not be dropped or observed links may not always corresponds to a valid relationship. In order to represent and reason with these types of uncertainty, we move beyond the discrete graph framework and develop social network measures based on a probabilistic graph representation. More specifically, we develop measures of path length, betweenness centrality, and clustering coefficient---one set based on sampling and one based on probabilistic paths. We evaluate our methods on three real-world networks from Enron, Facebook, and DBLP, showing that our proposed methods more accurately capture salient effects without being susceptible to local noise, and that the resulting analysis produces a better understanding of the graph structure and the uncertainty resulting from its change over time.

ReportDOI
TL;DR: The ways the software ORA (developed by CASOS at Carnegie Mellon University) handles the most important network measures in case of weighted, asymmetric, self-looped, and disconnected networks are described and discussed.
Abstract: : When Linton C. Freeman made his conceptual clarifications about centrality measures in social network analysis in 1979 he exclusively focused on unweighted, symmetric, and connected networks without the possibility of self-loops. Even though a lot of articles have been published in the last years discussing network measures for weighted, asymmetric or unconnected networks, the vast majority of researchers dealing with social network data simplify their networks based on Freeman's 1979 definitions before they calculate centrality measures. When dealing with weighted and/or asymmetric networks which can have self links and consist of multiple components, researchers are confronted with a lack of standardization. Different tools for social network analysis treat specific cases differently. In this article we describe and discuss the ways the software ORA (developed by CASOS at Carnegie Mellon University) handles the most important network measures in case of weighted, asymmetric, self-looped, and disconnected networks. In the center of our attention are the following measures, degree centrality, closeness centrality, betweenness centrality, eigenvector centrality, and clustering coefficient.

Proceedings Article
01 Dec 2011
TL;DR: This paper calculates and normalizes the three centrality measures values for each node in the Fuzzy Cognitive Map and transforms these values into linguistic terms using 2-tuple fuzzy linguistic representation model, and provides new important measures to overcome the above drawbacks.
Abstract: The Fuzzy Cognitive Map (FCM) provides a robust model for knowledge representation. FCM is a fuzzy signed weighted directed graph that depicts the knowledge of the domain as nodes representing the factors of the domain and arcs representing the connections among these factors. The centrality of a node in FCM, also called the importance of a node in this paper, is considered the most important index of all the graph theory indices applying to FCM which helps decision makers in analysing their FCM models. By finding the centrality values of the nodes in FCM, the important (central) nodes, which are the focal point for decision makers, are determined. The highest centrality value of a node in FCM is the most important one. Little research has addressed the centrality of the nodes in an FCM using only the degree centrality measure. The degree centrality measure only accounts for the direct connections of the node. Although the degree centrality index is considered an important measure in determining the centrality of a node in an FCM, it is not sufficient and has significant shortcomings; it ignores the importance of the indirect connections, the role of the node's position and flow of information through that node, i.e., how a node is close to other nodes and how the node contributes to the flow of information (communication control) through that node. In the literature, there are other centrality measures that can handle direct and indirect connections to determine the central nodes in a directed graph. This paper presents a new method for identifying the central nodes in an FCM. In order to achieve that, we provide, in addition to the degree measure, new important measures to overcome the above drawbacks. These new centrality measures are: betweenness and closeness measures. In this paper, we calculate and normalize the three centrality measures values for each node in the FCM. These values are then transformed into linguistic terms using 2-tuple fuzzy linguistic representation model. We use the 2-tuple model because it describes the granularity of uncertainty of the fuzzy sets and avoids the loss of information resulted from the imprecision and normalization of the measures. The calculated centrality measures values for each node in the FCM are then aggregated using a 2-tuple fuzzy fusion approach to obtain consensus centrality measure. The resulting aggregated values are then ranked in descending order to identify the most central nodes in the FCM, and this would improve the decision-making and help in simplify the FCM by removing the least important nodes from it. Finally, a list of future works related to this paper is suggested.

Proceedings ArticleDOI
12 Sep 2011
TL;DR: A new measure for centrality is proposed, based not on connectedness but on trust, which reflects this paradigm shift in face book-style online social networks.
Abstract: Centrality is an important element of social network analysis (SNA) measuring the relative power and influence of members of a social network. In face book-style online social networks every member is potentially able to communicate with everyone else within the network. This has an important impact on centrality: the power derivable from (exclusive) connections within the social graph is reduced because network members must not necessarily follow links. In this paper we propose a new measure for centrality which reflects this paradigm shift. It is based not on connectedness but on trust. We discuss different notions of trust, introduce trust matrix and trust centrality and provide an algorithm for its calculation.

Proceedings ArticleDOI
25 Jul 2011
TL;DR: A time-variant approach to degree centrality measure - time scale degreeCentrality (TSDC), which considers both presence and duration of links among actors within a network, whereas, the traditional degree centralism approach regards only the presence or absence of links.
Abstract: In this paper, we introduce a time-variant approach to degree centrality measure - time scale degree centrality (TSDC), which considers both presence and duration of links among actors within a network, whereas, the traditional degree centrality approach regards only the presence or absence of links. We illustrate the difference between traditional and time scale degree centrality measure by applying these two approaches to explore the impact of 'degree' attributes of doctor-patient network that evolves during patient hospitalization period on the hospital length of stay (LOS) both in macro- and micro-level. In macro-level, both the traditional and time-scale approaches to degree centrality can explain the relationship between the 'degree' attribute of doctor-patient network and LOS. However, at micro-level or small cluster level, TSDC provides better explanation while traditional degree centrality approach is impotent to explain the relationship between them.

Book ChapterDOI
24 May 2011
TL;DR: A new influence propagation model is proposed to describe the propagation of pre-defined importance over individual nodes and groups accompanied with random walk paths, and a new IPRank algorithm is proposed for ranking both individuals and groups.
Abstract: Ranking the centrality of a node within a graph is a fundamental problem in network analysis. Traditional centrality measures based on degree, betweenness, or closeness miss to capture the structural context of a node, which is caught by eigenvector centrality (EVC) measures. As a variant of EVC, PageRank is effective to model and measure the importance of web pages in the web graph, but it is problematic to apply it to other link-based ranking problems. In this paper, we propose a new influence propagation model to describe the propagation of pre-defined importance over individual nodes and groups accompanied with random walk paths, and we propose new IPRank algorithm for ranking both individuals and groups. We also allow users to define specific decay functions that provide flexibility to measure link-based centrality on different kinds of networks. We conducted testing using synthetic and real datasets, and experimental results show the effectiveness of our method.

Proceedings ArticleDOI
17 Mar 2011
TL;DR: This work quantified the importance of a node that its centrality index implicates and proposes a new type of betweenness centrality that is based on the flow circulating in a network.
Abstract: Network centrality indices are quantification of the fact that some nodes/edges are more central or more important in a network than others. Different centrality indices are suitable for different applications, but most of them have structural significance and require that the network be connected. Most centrality measures are only definitions and there hasn't been much work done in measuring the effectiveness of the measure in describing a network's performance, robustness and survivability. In this work, we have quantified the importance of a node that its centrality index implicates. We have conducted empirical analysis on different network robustness measures. The contribution of a node to these measures is studied as a function of its centrality index. We also propose a new type of betweenness centrality that is based on the flow circulating in a network. We compare circulation-based betweenness, eigenvector and shortest-path based betweenness centralities using network average clustering and shortest-path based network efficiency. 1

Proceedings ArticleDOI
24 Mar 2011
TL;DR: This paper points out that these alternate versions of closeness centrality are not true extensions of closness centrality in the sense that they do not rank the vertices of connected graphs in the same way that closenesscentrality does.
Abstract: The concept of vertex centrality has long been studied in order to help understand the structure and dynamics of complex networks. It has found wide applicability in practical as well as theoretical areas. Closeness centrality is one of the fundamental approaches to centrality, but one difficulty with using it is that it degenerates for disconnected graphs. Some alternate versions of closeness centrality have been proposed which rectify this problem. This paper points out that these are not true extensions of closeness centrality in the sense that they do not rank the vertices of connected graphs in the same way that closeness centrality does.


Proceedings ArticleDOI
16 May 2011
TL;DR: A mathematical framework which allows considering a city as a geometrical continuum rather than a plain topological graph is introduced and the color plotting of the various centralities permits a visual analysis of the city and to diagnose local malfunctionings.
Abstract: Firstly introduced in social science, the notion of centrality has spread to the whole complex network science. A centrality is a measure that quantifies whether an element of a network is well served or not, easy to reach, necessary to cross. This article focuses on cities' street network (seen as a communication network). We redefine two classical centralities (the closeness and the straightness) and introduce the notion of simplest centrality. To this we introduce a mathematical framework which allows considering a city as a geometrical continuum rather than a plain topological graph. The color plotting of the various centralities permits a visual analysis of the city and to diagnose local malfunctionings. The relevance of our framework and centralities is discussed from visual analysis of French towns and from computational complexity.

Journal ArticleDOI
TL;DR: Several centrality measures are analyzed by giving a general framework that includes the Bonacich centrality, PageRank centrality or in-degree vector, among others, by giving some geometrical characterizations and some deviation results that help to quantify the error of approximating a spectral centrality by a local estimator.

Dissertation
01 Jan 2011
TL;DR: It is argued that rumor centrality is correctly quantifying the influence of users on Twitter, and the leader-follower algorithm (LFA) does a better job of learning community structure on real social and biological networks than more common algorithms such as spectral clustering.
Abstract: Network centrality is a function that takes a network graph as input and assigns a score to each node. In this thesis, we investigate the potential of network centralities for addressing inference questions arising in the context of large-scale networked data. These questions are particularly challenging because they require algorithms which are extremely fast and simple so as to be scalable, while at the same time they must perform well. It is this tension between scalability and performance that this thesis aims to resolve by using appropriate network centralities. Specifically, we solve three important network inference problems using network centrality: finding rumor sources, measuring influence, and learning community structure. We develop a new network centrality called rumor centrality to find rumor sources in networks. We give a linear time algorithm for calculating rumor centrality, demonstrating its practicality for large networks. Rumor centrality is proven to be an exact maximum likelihood rumor source estimator for random regular graphs (under an appropriate probabilistic rumor spreading model). For a wide class of networks and rumor spreading models, we prove that it is an accurate estimator. To establish the universality of rumor centrality as a source estimator, we utilize techniques from the classical theory of generalized Polya's urns and branching processes. Next we use rumor centrality to measure influence in Twitter. We develop an influence score based on rumor centrality which can be calculated in linear time. To justify the use of rumor centrality as the influence score, we use it to develop a new network growth model called topological network growth. We find that this model accurately reproduces two important features observed empirically in Twitter retweet networks: a power-law degree distribution and a superstar node with very high degree. Using these results, we argue that rumor centrality is correctly quantifying the influence of users on Twitter. These scores form the basis of a dynamic influence tracking engine called Trumor which allows one to measure the influence of users in Twitter or more generally in any networked data. Finally we investigate learning the community structure of a network. Using arguments based on social interactions, we determine that the network centrality known as degree centrality can be used to detect communities. We use this to develop the leader-follower algorithm (LFA) which can learn the overlapping community structure in networks. The LFA runtime is linear in the network size. It is also non-parametric, in the sense that it can learn both the number and size of communities naturally from the network structure without requiring any input parameters. We prove that it is very robust and learns accurate community structure for a broad class of networks. We find that the LFA does a better job of learning community structure on real social and biological networks than more common algorithms such as spectral clustering. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)

Proceedings ArticleDOI
20 Jun 2011
TL;DR: Through empirical evaluation over example and real world networks, it is demonstrated how structural centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchoff index, is appropriately sensitive to perturbations/rewirings in thenetwork.
Abstract: We explore the geometry of networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian (L+). The reciprocal of squared distance from each node i to the origin in this n-dimensional space yields a structural centrality index (C*(i)) for the node, while the harmonic sum of individual node structural centrality indices, Pi 1/C * (i), i.e. the trace of L+, yields the well-known Kirchoff index (K), an overall structural descriptor for the network. In addition to its geometric interpretation, we provide alternative interpretation of the proposed structural centrality index (C*(i)) of each node in terms of forced detour costs and recurrences in random walks and electrical networks. Through empirical evaluation over example and real world networks, we demonstrate how structural centrality is better able to distinguish nodes in terms of their structural roles in the network and, along with Kirchoff index, is appropriately sensitive to perturbations/rewirings in the network.

Journal ArticleDOI
30 Apr 2011
TL;DR: This short paper explores random networks of the size around n = 100,000 by Monte-Carlo method and proposes Monte- carlo algorithms of computing closeness and betweenness centrality measures to study the small world properties of social networks.
Abstract: From a social network of n nodes connected by l lines, one may produce centrality measures such as closeness, betweenness and so on. In the past, the magnitude of n was around 1,000 or 10,000 at most. Nowadays, some networks have 10,000, 100,000 or even more than that. Thus, the scalability issue needs the attention of researchers. In this short paper, we explore random networks of the size around n = 100,000 by Monte-Carlo method and propose Monte-Carlo algorithms of computing closeness and betweenness centrality measures to study the small world properties of social networks.

Wise Lab1
01 Jan 2011
TL;DR: The study shows that the overall co-citation network is a small-world and scale-free network that has a relatively small number of nodes with high betweenness centrality and most nodes have low betweeness centrality scores.
Abstract: To investigate statistical characteristics of an evolving co-citation network,primarily in term of the dynamics of betweenness centrality measures,we generate co-citation network of papers published in journal of Scientometrics,and character the citations with high cited times or high betweenness centrality in the network.Our study shows that the overall co-citation network is a small-world and scale-free network.The co-citation network has a relatively small number of nodes with high betweenness centrality,most nodes have low betweeness centrality scores.Furthermore,the betweenness centrality distribution of the co-citation network follows Zipf-Pareto distribution.

Book ChapterDOI
12 Sep 2011
TL;DR: This study explores the evolution of a co-authorship network over time and finds that while the association between number of new attached nodes to an existing node and all its main centrality measures is almost positive and significant, the betweenness centrality correlation coefficient is always higher and increasing as network evolved over time.
Abstract: Complex networks (systems) as a phenomenon can be observed by a wide range of networks in nature and society. There is a growing interest to study complex networks from the evolutionary and behavior perspective. Studies on evolving dynamical networks have been resulted in a class of models to explain their evolving dynamic behavior that indicate a new node attaches preferentially to some old nodes in the network based on their number of links. In this study, we aim to explore if there are any other characteristics of the old nodes which affect on the preferential attachment of new nodes. We explore the evolution of a co-authorship network over time and find that while the association between number of new attached nodes to an existing node and all its main centrality measures (i.e., degree, closeness and betweenness) is almost positive and significant but betweenness centrality correlation coefficient is always higher and increasing as network evolved over time. Identifying the attachment behavior of nodes in complex networks (e.g., traders, disease propagation and emergency management) help policy and decision makers to focus on the nodes (actors) in order to control the resources distribution, information dissemination, disease propagation and so on due to type of the network.

01 Oct 2011
TL;DR: In this paper, a series of network descriptors based on betweenness centrality and transmission are proposed and their extremal values as well as some graphs to which they correspond are given.
Abstract: Transmission and betweenness centrality are key concepts in communication networks theory. In this paper, a series of network descriptors based on betweenness centrality and transmission are proposed. Their extremal values as well as some graphs to which they correspond are given.

Proceedings ArticleDOI
24 Sep 2011
TL;DR: Experimental results indicated that degree centrality and closeness centrality were effective measure in studying the center position and function of the nodes in BBS reply networks.
Abstract: In this paper, a reply network was constructed with the data downloaded from SINA BBS. Based on the complex network theory, we firstly studied the node closeness centrality and graph closeness centralization of the reply network, and analyzed the influence of the central figure in reply network by studying the node closeness centrality. The leadership of the central figure was proved through experimental validation method. Then the correlation of degree and average closeness centrality was discussed. Finally, a conclusion was drawn that degree and average closeness centrality are positive correlation. Experimental results indicated that degree centrality and closeness centrality were effective measure in studying the center position and function of the nodes in BBS reply networks.

Journal ArticleDOI
TL;DR: This paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability, finding that the two quantities vary independently.
Abstract: Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks, this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.

01 Jan 2011
TL;DR: Eigenvector centrality takes into account the centralityvalue of the neighbours of a node to assign a centrality value to it and this value can be utilized to select relay nodes in a delay tolerant network and improve the delivery delay.
Abstract: Centrality measure is an important concept in networks. It indicates the relative importance of nodes in a network. Various centrality measures have been proposed in the literature, such as degree centrality, closeness centrality etc. Practically all these measures are some values based on the properties of the node concerned. Eigenvector centrality takes into account the centrality value of the neighbours of a node to assign a centrality value to it. In this paper, we show how this value can be utilized to select relay nodes in a delay tolerant network and improve the delivery delay.