Katz centrality

About: Katz centrality is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 77858 citations.

From Affiliation Matrices to Adjacency Matrices: Methods and Techniques for the Analysis of Centrality

Abstract: In the analysis of 2-mode networks, the transition from affiliation matrices to adjacency matrices formalizes the information on overall actors' participation in the occasions, in a way that does not allow to exploit the whole amount of information in some analysis, such as centrality. In this article, I propose a procedure for the calculation of a different and more informative adjacency matrix; moreover, I propose an adaptation for Freeman centrality indices; this adaptation accounts for the different organization of the information on the intersubset ties, which allows the computation of centrality using all the available information. Finally, I empirically illustrate the introduced procedures, and the information they allow to retrieve, analyzing a real 2-mode network known in the literature.

Map equation centrality: community-aware centrality based on the map equation

Abstract: Abstract To measure node importance, network scientists employ centrality scores that typically take a microscopic or macroscopic perspective, relying on node features or global network structure. However, traditional centrality measures such as degree centrality, betweenness centrality, or PageRank neglect the community structure found in real-world networks. To study node importance based on network flows from a mesoscopic perspective, we analytically derive a community-aware information-theoretic centrality score based on network flow and the coding principles behind the map equation: map equation centrality. Map equation centrality measures how much further we can compress the network’s modular description by not coding for random walker transitions to the respective node, using an adapted coding scheme and determining node importance from a network flow-based point of view. The information-theoretic centrality measure can be determined from a node’s local network context alone because changes to the coding scheme only affect other nodes in the same module. Map equation centrality is agnostic to the chosen network flow model and allows researchers to select the model that best reflects the dynamics of the process under study. Applied to synthetic networks, we highlight how our approach enables a more fine-grained differentiation between nodes than node-local or network-global measures. Predicting influential nodes for two different dynamical processes on real-world networks with traditional and other community-aware centrality measures, we find that activating nodes based on map equation centrality scores tends to create the largest cascades in a linear threshold model.

Investigating Journal Citation Network with Centrality Measures in the Public Administration and Policy Field

Abstract: Writing high-quality papers and publishing them at prestigious academic journals would be something that every scholar strives for. This study made a network with nine academic journals in South Korea in the field of public administration and public policy and analyzed the influence of academic journals through social network analysis. Using centrality measures, such as degree centrality, beta centrality, and eigenvector centrality, this study found that Korean Public Administration Review has the highest influence on the journal network, followed by Korean Public Studies Review. However, different choice of centrality measure led to different ranking of journals in terms of their influence.

Game-Theoretic Centrality Measures for Weighted Graphs

Abstract: The betweenness centrality is one of the basic concepts in the analysis of the social networks. Initial definition for the betweenness of a node in the graph is based on the fraction of the number of geodesics (shortest paths) between any two nodes that given node lies on, to the total number of the shortest paths connecting these nodes. This method has polynomial complexity. We propose a new concept of the betweenness centrality for weighted graphs using the methods of cooperative game theory. The characteristic function is determined by special way for different coalitions (subsets of the graph). Two approaches are used to determine the characteristic function. In the first approach the characteristic function is determined via the number of direct and indirect weighted connecting paths in the coalition. In the second approach the coalition is considered as an electric network and the characteristic function is determined as a total current in this network. We use the Kirchhoff's law. After that the betweenness centrality is determined as the Myerson value. The results of computer simulations for some examples of networks, in particular, for the popular social network "VKontakte", as well as the comparing with the PageRank method are presented.

Fast Exact and Approximate Computation of Betweenness Centrality in Social Networks

Abstract: Social networks have demonstrated in the last few years to be a powerful and flexible concept useful to represent and analyze data emerging from social interactions and social activities. The study of these networks can thus provide a deeper understanding of many emergent global phenomena. The amount of data available in the form of social networks is growing by the day. This poses many computational challenging problems for their analysis. In fact many analysis tools suitable to analyze small to medium sized networks are inefficient for large social networks. The computation of the betweenness centrality index (BC) is a well established method for network data analysis and it is also important as subroutine in more advanced algorithms, such as the Girvan-Newman method for graph partitioning. In this chapter we present a novel approach for the computation of the betweenness centrality, which speeds up considerably Brandes’ algorithm (the current state of the art) in the context of social networks. Our approach exploits the natural sparsity of the data to algebraically (and efficiently) determine the betweenness of those nodes forming trees (tree-nodes) in the social network. Moreover, for the residual network, which is often of much smaller size, we modify directly the Brandes’ algorithm so that we can remove the nodes already processed and perform the computation of the shortest paths only for the residual nodes. We also give a fast sampling-based algorithm that computes an approximation of the betweenness centrality values of the residual network while returns the exact value for the tree-nodes. This algorithm improves in speed and precision over current state of the art approximation methods. Tests conducted on a sample of publicly available large networks from the Stanford repository show that, for the exact algorithm, speed improvements of a factor ranging between 2 and 5 are possible on several such graphs, when the sparsity, measured by the ratio of tree-nodes to the total number of nodes, is in a medium range (30–50 %). For some large networks from the Stanford repository and for a sample of social networks provided by Sistemi Territoriali with high sparsity (80 % and above) tests show that our algorithm, named SPVB (for Shortest Path Vertex Betweenness), consistently runs between one and two orders of magnitude faster than the current state of the art exact algorithm.