Katz centrality

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

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.

Covertness Centrality in Networks

Abstract: It has been known for some time that in terror networks, money laundering networks, and criminal networks, "important" players want to stay "off" the radar. They need sufficient centrality (according to traditional measures) to be well connected with the rest of their network, but need to blend in with the crowd. In this paper, we propose the concept of covertness centrality (CC). The covertness centrality of a vertex v consists of two parts: how "common" v is w.r.t. a set C of centrality measures, and how well v can "communicate" with a user-specified set of vertices. The more "common" v is, the more able it is to stay hidden in a crowd. Given C, we first propose some general properties we would like a common-ness measure to satisfy. We then develop a probabilistic model of common-ness that a vertex has w.r.t. C (specifying, intuitively, how many other vertices are like it according to all centrality measures in C). Covertness centrality of vertex v is then defined as a linear combination of common-ness and the ability of v to communicate with a user-specified set of other vertices. We develop a prototype implementation of CC and report on experiments we have conducted with it on several real-world data sets.

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.

A Dynamic Algorithm for Updating Katz Centrality in Graphs

Abstract: Many large datasets from a variety of fields of research can be represented as graphs. A common query is to identify the most important, or highly ranked, vertices in a graph. Centrality metrics are used to obtain numerical scores for each vertex in the graph. The scores can then be translated to rankings identifying relative importance of vertices. In this work we focus on Katz Centrality, a linear algebra based metric. In many real applications, since data is constantly being produced and changed, it is necessary to have a dynamic algorithm to update centrality scores with minimal computation when the graph changes. We present an algorithm for updating Katz Centrality scores in a dynamic graph that incrementally updates the centrality scores as the underlying graph changes. Our proposed method exploits properties of iterative solvers to obtain updated Katz scores in dynamic graphs. Our dynamic algorithm improves performance and achieves speedups of over two orders of magnitude compared to a standard static algorithm while maintaining high quality of results.

Network Centrality, Measures of

Abstract: Measures of network centrality assess the importance of elements in arrays of relationships linking entities, such as persons, organizations, or documents. Important entities may have many contacts, be related to other important entities, be near other entities, or be positioned between others. Most centrality measures refer to entities, but some refer to relationships. Network-level centralization statistics measure variation in centrality across entities within a network. This article presents centrality measures for common forms of network data, including undirected binary networks, valued networks, directed networks, and two-mode networks of relationships that connect distinct types of entities.