Showing papers on "Katz centrality published in 2013"

Total communicability as a centrality measure

Abstract: We examine node centrality measures based on the notion of total communicability, defined in terms of the row sums of matrix functions of the adjacency matrix of the network. Our main focus is on the matrix exponential and the resolvent, which have natural interpretations in terms of walks on the underlying graph. While such measures have been used before for ranking nodes in a network, we show that they can be computed very rapidly even in the case of large networks. Furthermore, we propose the (normalized) total sum of node communicabilities as a useful measure of network connectivity. Extensive numerical studies are conducted in order to compare this centrality measure with the closely related ones of subgraph centrality [E. Estrada and J. A. Rodriguez-Velazquez, Phys. Rev. E, 71 (2005), 056103] and Katz centrality [L. Katz, Psychometrica, 18 (1953), pp. 39–43]. Both synthetic and real-world networks are used in the computations.

Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks

Abstract: A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Understanding Urban Traffic-Flow Characteristics: A Rethinking of Betweenness Centrality

Abstract: In this study we estimate urban traffic flow using GPS-enabled taxi trajectory data in Qingdao, China, and examine the capability of the betweenness centrality of the street network to predict traf...

A modified evidential methodology of identifying influential nodes in weighted networks

Abstract: How to identify influential nodes in complex networks is still an open hot issue. In the existing evidential centrality (EVC), node degree distribution in complex networks is not taken into consideration. In addition, the global structure information has also been neglected. In this paper, a new Evidential Semi-local Centrality (ESC) is proposed by modifying EVC in two aspects. Firstly, the Basic Probability Assignment (BPA) of degree generated by EVC is modified according to the actual degree distribution, rather than just following uniform distribution. BPA is the generation of probability in order to model uncertainty. Secondly, semi-local centrality combined with modified EVC is extended to be applied in weighted networks. Numerical examples are used to illustrate the efficiency of the proposed method.

Identifying high betweenness centrality nodes in large social networks

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. The randomized algorithm runs in time O(κ3 n 2−2αlog n) and outputs, for each vertex v, an estimate of its κ-path centrality up to additive error of ±n 1/2+α with probability 1 − 1/n 2. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms.

A matrix iteration for dynamic network summaries

Abstract: We propose a new algorithm for summarizing properties of large-scale time-evolving networks. This type of data, recording connections that come and go over time, is generated in many modern applications, including telecommunications and online human social behavior. The algorithm computes a dynamic measure of how well pairs of nodes can communicate by taking account of routes through the network that respect the arrow of time. We take the conventional approach of downweighting for length (messages become corrupted as they are passed along) and add the novel feature of downweighting for age (messages go out of date). This allows us to generalize widely used Katz-style centrality measures that have proved popular in network science to the case of dynamic networks sampled at nonuniform points in time. We illustrate the new approach on synthetic and real data.

Seeing the Bigger Picture: How Nodes Can Learn Their Place Within a Complex Ad Hoc Network Topology

Abstract: This article explained how nodes in a network graph can infer information about the network topology or its topology related properties, based on in-network distributed learning, i.e., without relying on an external observer who has a complete overview over the network. Some key concepts from the field of SGT were reviewed, with a focus on those that allow for a simple distributed implementation, i.e., eigenvector or Katz centrality, algebraic connectivity, and the Fiedler vector. This paper also explained how the nodes themselves can quantify their individual network-wide influence, as well as identify densely connected node clusters and the sparse bridge links between them. The addressed concepts, as well as more advanced concepts from the field of SGT, are believed to be crucial catalysts in the design of topology-aware distributed algorithms. Examples were provided on how these techniques can be exploited in several nontrivial distributed signal processing tasks.

A new approach to identify influential spreaders in complex networks

Abstract: In the research of the propagation model of complex network, it is of theoretical and practical significance to detect the most influential spreaders. Global metrics such as degree centrality, closeness centrality, betweenness centrality and K-shell centrality can be used to identify the influential spreaders. These approaches are simple but have low accuracy. We propose K-shell and Community centrality (KSC) model. This model considers not only the internal properties of nodes but also the external properties of nodes, such as the com-munity which these nodes belong to. The Susceptible-Infected-Recovered (SIR) model is used to evaluate the performance of KSC model. The experiment result shows that our method is better to identify the most influential nodes. This paper comes up with a new idea and method for the study in this field.

A matrix analysis of different centrality measures.

Abstract: Node centrality measures including degree, eigenvector, Katz and subgraph centralities are analyzed for both undirected and directed networks. We show how parameter-dependent measures, such as Katz and subgraph centrality, can be "tuned" to interpolate between degree and eigenvector centrality, which appear as limiting cases of the other measures. We interpret our finding in terms of the local and global influence of a given node in the graph as measured by graph walks of different length through that node. Our analysis gives some guidance for the choice of parameters in Katz and subgraph centrality, and provides an explanation for the observed correlations between different centrality measures and for the stability exhibited by the ranking vectors for certain parameter ranges. The important role played by the spectral gap of the adjacency matrix is also highlighted.

Hybrid Centrality Measures for Binary and Weighted Networks

Abstract: Existing centrality measures for social network analysis suggest the importance of an actor and give consideration to actor’s given structural position in a network. These existing measures suggest specific attribute of an actor (i.e., popularity, accessibility, and brokerage behavior). In this study, we propose new hybrid centrality measures (i.e., Degree-Degree, Degree-Closeness and Degree-Betweenness), by combining existing measures (i.e., degree, closeness and betweenness) with a proposition to better understand the importance of actors in a given network. Generalized set of measures are also proposed for weighted networks. Our analysis of co-authorship networks dataset suggests significant correlation of our proposed new centrality measures (especially weighted networks) than traditional centrality measures with performance of the scholars. Thus, they are useful measures which can be used instead of traditional measures to show prominence of the actors in a network.

Terrorist Networks, Network Energy and Node Removal: A New Measure of Centrality Based on Laplacian Energy

Abstract: In this work we propose a centrality measure for networks, which we refer to as Laplacian centrality, that provides a general framework for the centrality of a vertex based on the idea that the importance (or centrality) of a vertex is related to the ability of the network to respond to the deactivation or removal of that vertex from the network. In particular, the Laplacian centrality of a vertex is defined as the relative drop of Laplacian energy caused by the deactivation of this vertex. The Laplacian energy of network G with n vertices is defined as , where is the eigenvalue of the Laplacian matrix of G. Other dynamics based measures such as that of Masuda and Kori and PageRank compute the importance of a node by analyzing the way paths pass through a node while our measure captures this information as well as the way these paths are “redistributed” when the node is deleted. The validity and robustness of this new measure are illustrated on two different terrorist social network data sets and 84 networks in James Moody’s Add Health in school friendship nomination data, and is compared with other standard centrality measures.

Methods to find community based on edge centrality

Abstract: Divisive algorithms are of great importance for community detection in complex networks. One algorithm proposed by Girvan and Newman (GN) based on an edge centrality named betweenness, is a typical representative of this field. Here we studied three edge centralities based on network topology, walks and paths respectively to quantify the relevance of each edge in a network, and proposed a divisive algorithm based on the rationale of GN algorithm for finding communities that removes edges iteratively according to the edge centrality values in a certain order. In addition, we gave a comparison analysis of these measures with the edge betweenness and information centrality. We found the principal difference among these measures in the partition procedure is that the edge centrality based on walks first removes the edge connected with a leaf vertex, but the others first delete the edge as a bridge between communities. It indicates that the edge centrality based on walks is harder to uncover communities than other edge centralities. We also tested these measures for community detection. The results showed that the edge information centrality outperforms other measures, the edge centrality based on walks obtains the worst results, and the edge betweenness gains better performance than the edge centrality based on network topology. We also discussed our method’s efficiency and found that the edge centrality based on walks has a high time complexity and is not suitable for large networks.

Weighted node degree centrality for hypergraphs

Abstract: Many real-world social interactions involve multiple people, for e.g., authors collaborating on a paper, email exchanges made in a company and task-oriented teams in workforce. Simple graph representation of these activities destroys the group structure present in them. Hypergraphs have recently emerged as a better tool for modeling group interactions. However, methods in social hypernetwork analysis haven't kept pace. In this work, we extend the concept of node degree centrality to hypergraphs. We validate our proposed measures using alternate measures of influence available to us using two datasets namely, the DBLP dataset of scientific collaborations and the group network in a popular Chinese multi-player online game called CR3. We discuss several schemes for assigning weights to hyperedges and compare them empirically. Finally, we define separate weak and strong tie node degree centralities which improves performance of our models. Weak tie degree centrality is found to be a better predictor of influence in hypergraphs than strong tie degree centrality.

h-Type hybrid centrality measures for weighted networks

Abstract: In this study, new centrality (collaborative) measures are proposed for a node in weighted networks in three different categories. The bibliometric indicators' concepts (e.g., h-index and g-index) are applied to the network analysis measures in order to introduce the new centrality measures. First category of measures (i.e., l-index, al-index and gl-index) only considers a node's neighbors' degree. Second category of measures (i.e., h-Degree, a-Degree and g-Degree) takes into account the links' weights of a node in a weighted network. Third category of measures (i.e., Hw-Degree, Aw-Degree and Gw-Degree) combines both neighbors' degree and their links' weight. Using a co-authorship network, the association between these new measures and the existing measures with scholars' performance is examined to show the applicability of the new centrality measures. The analysis shows that the scholars' citation-based performances measures are significantly associated with all the proposed centrality measures but the correlation coefficient for the ones based on average indicators (i.e., a-Degree and Aw-Degree) is the highest.

"Follow the leader": a centrality guided clustering and its application to social network analysis.

Abstract: Within graph theory and network analysis, centrality of a vertex measures the relative importance of a vertex within a graph. The centrality plays key role in network analysis and has been widely studied using different methods. Inspired by the idea of vertex centrality, a novel centrality guided clustering (CGC) is proposed in this paper. Different from traditional clustering methods which usually choose the initial center of a cluster randomly, the CGC clustering algorithm starts from a “LEADER”—a vertex with the highest centrality score—and a new “member” is added into the same cluster as the “LEADER” when some criterion is satisfied. The CGC algorithm also supports overlapping membership. Experiments on three benchmark social network data sets are presented and the results indicate that the proposed CGC algorithm works well in social network clustering.

Lobby index as a network centrality measure

Abstract: We study the lobby index (l-index for short) as a local node centrality measure for complex networks. The l-index is compared with degree (a local measure), betweenness and Eigenvector centralities (two global measures) in the case of a biological network (Yeast interaction protein–protein network) and a linguistic network (Moby Thesaurus II). In both networks, the l-index has a poor correlation with betweenness but correlates with degree and Eigenvector centralities. Although being local, the l-index carries more information about its neighbors than degree centrality. Also, it requires much less time to compute when compared with Eigenvector centrality. Results show that the l-index produces better results than degree and Eigenvector centrality for ranking purposes.

Neighbor vector centrality of complex networks based on neighbors degree distribution

Abstract: We introduce a novel centrality metric, the neighbor vector centrality. It is a measurement of node importance with respect to the degree distribution of the node neighbors. This centrality is explored in the context of several networks. We use attack vulnerability simulation to compared our approach with three standard centrality approaches. While for real-world network our method outperforms the other three metrics, for synthetic networks it shows a slightly weak properties but still a good measure overall. There is no significant correlation of our method with network size, average degree or assortativity. In summary, neighbor vector centrality presents a novel measurement of node importance, which has a better performance to reduce dynamics of real-world complex networks.

Leader election on tree-based centrality in ad hoc networks

Abstract: A leader in a network plays important roles for various services of the network and controls problems of the network. Therefore, when the nodes with high centrality are selected as the leader nodes in the network, the network can be more efficiently controlled, and the amount of wasted resources can be reduced. In this study, we propose a novel method for determining leader nodes by measuring centrality of nodes in the ad hoc networks. The proposed method can obtain the centrality of each node using the average depth of nodes based on the tree topology. Consequently, the amount of the information required for leader election becomes smaller and the calculation process is also simpler, compared with those of representative centrality methods in social network analysis (SNA). In the experiment, the proposed tree-based centrality technique is compared with the well-known centrality schemes such as degree, closeness, and betweenness. The proposed tree-based centrality method has similar centrality priority as degree, closeness, and betweenness and also has better performance in the comparison of the control messages generated.

Embeddedness of European Regions in EU Funded R&D Networks: A Spatial Econometric Perspective

Abstract: This study focuses on the embeddedness of regions in R&D networks within the EU Framework Programmes (FPs). Embeddedness denotes a region’s position in terms of graph theoretic centrality measures. We use betweenness centrality as a proxy for the ability to control knowledge flows in networks, and eigenvector centrality to measure intensive participation and connectedness with central hubs. The centrality measures are calculated at the organisational level to reflect relevant network structures, and then aggregated to the region. The objective is to estimate how region-internal and region-external characteristics affect a region’s network embeddedness, using panel spatial Durbin error models (SDEM). The results reveal that R&D expenditures, the strength of the knowledge base and a region’s socio-economic potential enable high network embeddedness in general. More specifically, a region’s importance in the network weighted by its linkages to central hubs (eigenvector centrality) is notably determined by a region’s endowment with human capital, while a diversified technological and economic structure is conducive to accessing and controlling diverse knowledge flows (betweenness centrality) in the European network of R&D collaboration.

On the limiting behavior of parameter-dependent network centrality measures

Abstract: We consider a broad class of walk-based, parameterized node centrality measures for network analysis. These measures are expressed in terms of functions of the adjacency matrix and generalize various well-known centrality indices, including Katz and subgraph centrality. We show that the parameter can be "tuned" to interpolate between degree and eigenvector centrality, which appear as limiting cases. Our analysis helps explain certain correlations often observed between the rankings obtained using different centrality measures, and provides some guidance for the tuning of parameters. We also highlight the roles played by the spectral gap of the adjacency matrix and by the number of triangles in the network. Our analysis covers both undirected and directed networks, including weighted ones. A brief discussion of PageRank is also given.

Alpha current flow betweenness centrality

Abstract: A class of centrality measures called betweenness centralities reflects degree of participation of edges or nodes in communication between different parts of the network. The original shortest-path betweenness centrality is based on counting shortest paths which go through a node or an edge. One of shortcomings of the shortest-path betweenness centrality is that it ignores the paths that might be one or two steps longer than the shortest paths, while the edges on such paths can be important for communication processes in the network. To rectify this shortcoming a current flow betweenness centrality has been proposed. Similarly to the shortest path betwe has prohibitive complexity for large size networks. In the present work we propose two regularizations of the current flow betweenness centrality, $\alpha$-current flow betweenness and truncated $\alpha$-current flow betweenness, which can be computed fast and correlate well with the original current flow betweenness.

Measuring Betweenness Centrality in Social Internetworking Scenarios

Abstract: The importance of the betweenness centrality measure in (on-line) social networks is well known, as well as its possible applications to various domains. However, the classical notion of betweenness centrality is not able to capture the centrality of nodes w.r.t. paths crossing different social networks. In other words, it is not able to detect those nodes of a multi-social-network scenario (called Social Internetworking Scenario) which play a central role in inter-social-network information flows. In this paper, we propose a new measure of betweenness centrality suitable for Social Internetworking Scenarios, also applicable to the case of different communities of the same social network. The new measure has been tested in a number of synthetic networks, highlighting the significance and effectiveness of our proposal.

A Closeness Centrality Analysis Algorithm for Workflow-supported Social Networks

Abstract: This paper proposes a closeness centrality analysis algorithm for workflow-supported social networks that represent the collaborative relationships among the performers who are involved in a specific workflow model. The proposed algorithm uses the social network analysis techniques, particularly closeness centrality equations, to analyze the closeness centrality of the workflow-supported social network. Additionally, through an example we try to verify the accuracy and appropriateness of the proposed algorithm.

Power indices of influence games and new centrality measures for social networks

Abstract: In social network analysis, there is a common perception that influence is relevant to determine the global behavior of the society and thus it can be used to enforce cooperation by targeting an adequate initial set of individuals or to analyze global choice processes. Here we propose centrality measures that can be used to analyze the relevance of the actors in process related to spread of influence. In (39) it was considered a multiagent system in which the agents are eager to perform a collective task depending on the perception of the willingness to perform the task of other individuals. The setting is modeled using a notion of simple games called influence games. Those games are defined on graphs were the nodes are labeled by their influence threshold and the spread of influence between its nodes is used to determine whether a coalition is winning or not. Influence games provide tools to measure the importance of the actors of a social network by means of classic power indices and provide a framework to consider new centrality criteria. In this paper we consider two of the most classical power indices, i.e., Banzhaf and Shapley-Shubik indices, as centrality measures for social networks in influence games. Although there is some work related to specific scenarios of game-theoretic networks, here we use such indices as centrality measures in any social network where the spread of influence phenomenon can be applied. Further, we define new centrality measures such as satisfaction and effort that, as far as we know, have not been considered so far. Besides the definition we perform a comparison of the proposed measures with other three classic centrality measures, degree, closeness and betweenness. To perform the comparison we consider three social networks. We show that in some cases our measurements provide centrality hierarchies similar to those of other measures, while in other cases provide different hierarchies.

A centrality measure for communication ability in weighted network

Abstract: This paper proposes a new node centrality measurement in a weighted network, the communication centrality, which is inspired by Hirsch’s h -index. We investigated the properties of the communication centrality, and proved that the distribution of the communication centrality has the power-law upper tail in weighted scale-free networks. Relevant measures for node and network are discussed as extensions. A case study of a scientific collaboration network indicates that the communication centrality is different from other common centrality measures and other h -type indexes. Communication centrality displays moderate correlation with other indexes, and contains a well-balanced mix of other centrality measures and cannot be replaced by any of them.

Efficient Algorithm for Destabilization of Terrorist Networks

Abstract: The advisory feasibility of Social Network Analysis (SNA) to study social networks have encouraged the law enforcement and security agencies to investigate the terrorist network and its behavior along with key players hidden in the web. The study of the terrorist network, utilizing SNA approach and Graph Theory where the network is visualized as a graph, is termed as Investigative Data Mining or in general Terrorist Network Mining. The SNA defined centrality measures have been successfully incorporated in the destabilization of terrorist network by deterring the dominating role(s) from the network. The destabilizing of the terrorist group involves uncovering of network behavior through the defined hierarchy of algorithms. This paper concerning the destabilization of terrorist network proposes a pioneer algorithm which seems to replace the already available hierarchy of algorithms. This paper also suggests use of the two influential centralities, PageRank Centrality and Katz Centrality, for effectively neutralizing of the network.

Application of entropy of centrality measures to routing in tactical wireless networks

Abstract: Various Centrality measures such as Degree, Closeness, and Betweenness were introduced in order to analyze networks and understand both the global dynamics of the networks and the roles played by individual nodes. It will be worthwhile to rank the centrality measures of each node and an index of the distribution of centrality measures in the entire network. In this paper, we define the notion of entropy of centrality measures, which extends the concept of centrality to the whole network. We show that this measure has wide range of applications, in network design, from designing maximally efficient networks to identifying dominance of one node or link in the context of entire network. In particular, we present an application to tactical wireless networks.