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Katz centrality

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


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Journal ArticleDOI
TL;DR: This work presents an algorithm for updating Katz centrality scores in a dynamic graph that incrementally updates thecentrality scores as the underlying graph changes, and exploits properties of iterative solvers to obtain updated Katz scores in dynamic graphs.
Abstract: A variety of large datasets, such as social networks or biological data, can be represented as graphs. A common query in graph analysis is to identify the most important vertices in a graph. Centrality metrics are used to obtain numerical scores for each vertex in the graph. The scores are then 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 are 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.

8 citations

Proceedings ArticleDOI
01 Dec 2014
TL;DR: Experimental results show that the proposed novel metric, k-hop centrality outperforms state-of-the-art methods in this field in terms of both infection ratios (spreading influence) and computational complexity.
Abstract: Identifying the most influential spreaders in social networks has many practical applications. The existing methods for the purpose are either too time-consuming for dynamic large-scale networks, such as betweenness centrality, closeness centrality, eigenvector centrality and Katz centrality, or do not consider the network topology, such as degree centrality. To design an effective method to identify the most influential nodes in a network, we propose a novel metric, k-hop centrality which is a generalization of degree centrality. The k-hop index is the summation of the number n(i) of nodes within k-hop distance from the node in question, attenuated by 1/αi, for 1 ≤ i ≤ k (α is the average degree of nodes in the network). It is calculated in a localized manner and is complexity-scalable by adjusting the value of k, thus suitable for dynamically changing, large social networks. We adopt the Susceptible Infected Recovered (SIR) model to evaluate the performance of k-hop centrality over four real datasets of complex networks, and experimental results show that our method outperforms state-of-the-art methods in this field in terms of both infection ratios (spreading influence) and computational complexity. Our work sheds some light on designing efficient spreading strategies for complex networks.

8 citations

Journal ArticleDOI
TL;DR: It is shown through some surprising examples that study of transmission behavior based solely on a graph’s topological and degree properties is lacking when it comes to modeling network propagation or conceptual (vs. physical) structure.
Abstract: A fundamental concept of social network analysis is centrality. Many analyses represent the network topology in terms of concept transmission/variation, e.g., influence, social structure, community or other aggregations. Even when the temporal nature of the network is considered, analysis is conducted at discrete points along a continuous temporal scale. Unfortunately, well-studied metrics of centrality do not take varying probabilities into account. The assumption that social and other networks that may be physically stationary, e.g., hard wired, are conceptually static in terms of information diffusion or conceptual aggregation (communities, etc.) can lead to incorrect conclusions. Our findings illustrate, both mathematically and experimentally, that if the notion of network topology is not stationary or fixed in terms of the concept, e.g., groups, belonging, community or other aggregations, centrality should be viewed probabilistically. We show through some surprising examples that study of transmission behavior based solely on a graph’s topological and degree properties is lacking when it comes to modeling network propagation or conceptual (vs. physical) structure.

8 citations

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.

8 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202318
202232
202114
202013
201919
201824