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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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Book ChapterDOI
16 May 2017
TL;DR: A novel vertex centrality measure based on the quantum information theoretical concept of Holevo quantity is proposed, which measures the importance of a vertex in terms of the variation in graph entropy before and after its removal from the graph.
Abstract: In recent years, the increasing availability of data describing the dynamics of real-world systems led to a surge of interest in the complex networks of interactions that emerge from such systems. Several measures have been introduced to analyse these networks, and among them one of the most fundamental ones is vertex centrality, which quantifies the importance of a vertex within a graph. In this paper, we propose a novel vertex centrality measure based on the quantum information theoretical concept of Holevo quantity. More specifically, we measure the importance of a vertex in terms of the variation in graph entropy before and after its removal from the graph. More specifically, we find that the centrality of a vertex v can be broken down in two parts: (1) one which is negatively correlated with the degree centrality of v, and (2) one which depends on the emergence of non-trivial structures in the graph when v is disconnected from the rest of the graph. Finally, we evaluate our centrality measure on a number of real-world as well as synthetic networks, and we compare it against a set of commonly used alternative measures.

3 citations

Proceedings ArticleDOI
14 Oct 2019
TL;DR: In this article, the authors define two variants of the potential gain, called the geometric and the exponential potential gain and present fast algorithms to compute them, which are the first instances of a novel class of composite centrality metrics, which combine the popularity of a node in G with its similarity to all other nodes.
Abstract: Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph G is navigable when an agent is able to efficiently reach any target node in G by means of local routing decisions. In a social network navigability translates to the ability of reaching an individual through personal contacts. Graph navigability is well-studied, but a fundamental question is still open: why are some individuals more likely than others to be reached via short, friend-of-a-friend, communication chains? In this article we answer the question above by proposing a novel centrality metric called the potential gain, which, in an informal sense, quantifies the easiness at which a target node can be reached. We define two variants of the potential gain, called the geometric and the exponential potential gain, and present fast algorithms to compute them. The geometric and the potential gain are the first instances of a novel class of composite centrality metrics, i.e., centrality metrics which combine the popularity of a node in G with its similarity to all other nodes. As shown in previous studies, popularity and similarity are two main criteria which regulate the way humans seek for information in large networks such as Wikipedia. We give a formal proof that the potential gain of a node is always equivalent to the product of its degree centrality (which captures popularity) and its Katz centrality (which captures similarity). CCS CONCEPTS • Information systems → Web crawling; Web indexing.

2 citations

Journal ArticleDOI
TL;DR: A combinatorial study on the rearrangement of links in the structure of directed networks for the purpose of improving the valuation of a vertex or group of vertices as established by an eigenvector-based centrality measure.

2 citations

Journal ArticleDOI
TL;DR: An evaluation of targeted attack sequences based on a new set of power traffic centrality measures according to the vulnerability prediction measure (VPM) approach finds the RMCEF strategy with degree, eigenvector and Katz centralities is a good estimation of the most harmful attack sequences on nodes and links with a shorter execution time than the IMDEF.
Abstract: This paper aims to present an evaluation of targeted attack sequences based on a new set of power traffic centrality measures according to the vulnerability prediction measure (VPM) approach. A framework for evaluation of attack proposed in previous work is applied using three fault strategies: remove most central element first (RMCEF), iterated most central element first, and iterated electrical most damaging element first (IMDEF). For attacks on nodes, the reliability of the IMDEF strategy is confirmed, as it was the most predictive in terms of the VPM. Nevertheless, in attacks performed on links, the IMDEF does not always represents the most harmful attack. Regarding the new centralities, the Katz centrality consistently presented high values of VPM for attacks on nodes and links, with results that are comparable to degree and eigenvector centralities. In terms of execution times, the percolation centrality is not recommended, as it presented the highest execution times. The RMCEF strategy with degree, eigenvector and Katz centralities is a good estimation of the most harmful attack sequences on nodes and links with a shorter execution time than the IMDEF.

2 citations

Dissertation
01 Jan 2000
TL;DR: In this paper, the authors examine the relative contributions of feature centrality and feature variability in property induction, whether centrality offers a domain-general or a domain specific constraint, and whether the centrality can operate under conditions of vagueness.
Abstract: This thesis examines property generalization among concepts. Its primary objective is to investigate the hypothesis that the more central a feature for a concept, the higher its generalizability to other concepts that share a similar structure (features and dependencies). Its secondary objectives are to examine the relative contributions of feature centrality and feature variability in property induction, whether centrality offers a domain-general or a domain-specific constraint, and whether centrality can operate under conditions of vagueness. Experiments 1 and 2 addressed the centrality hypothesis with centrality measured, whereas Experiments 3 to 14 and 17 with centrality manipulated. Relative feature centrality was manipulated as follows: from a single-dependency chain (Experiments 3 to 7), from the number of properties that depended upon a feature (Experiments 8 to 11 and 17), and from the centrality of the properties that depended upon the critical features (Experiments 12 to 14). The results support the centrality hypothesis. Experiments 12 to 16 addressed the relative contributions of centrality and variability in property induction. Experiments 12 to 14 pitted a central and variable property against a less central and less variable property in judgments of frequency and inductive strength. The results suggest that property induction depends on centrality rather than frequency information, and that centrality can bias the perception of frequency (although the latter results were not clear-cut). Experiments 15 and 16 pitted centrality against variability in information seeking. The results show that centrality information is sought more often than variability information to make an inference, especially amongst dissimilar concepts. Experiments 1 to 16 used animal categories. Experiment 17 examined the centrality hypothesis with artifact categories. The results show centrality effects. Taken together, the Experiments suggest that centrality offers a domain-general constraint. Experiments 5, 8 to 11, and 17 left the properties that depended upon a candidate feature unspecified. A centrality effect was still obtained. The results suggest that centrality can operate under conditions of vagueness. The results are discussed in terms of theories of conceptual structure and models of category-based inference. A model to capture the present findings is also sketched.

2 citations


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