Showing papers on "Katz centrality published in 2021"
TL;DR: This study presents an approach to develop and interpret multilayer networks in light of resilience engineering, and identifiesStrengths and weaknesses of social interactions at the ICU are discussed based on the adopted metrics.
10 citations
TL;DR: A novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity is proposed.
Abstract: Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE, a Sampling-based Algorithm for fast Katz centrality Estimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.
8 citations
TL;DR: In this article, a network-based modal analysis technique is presented to identify key dynamical paths along which perturbations amplify over a time-varying base flow.
Abstract: We present a network-based modal analysis technique that identifies key dynamical paths along which perturbations amplify over a time-varying base flow. This analysis is built upon the Katz centrality, which reveals the flow structures that can effectively spread perturbations over a time-evolving network of vortical interactions on the base flow. Motivated by the resolvent form of the Katz function, we take the singular value decomposition of the resulting communicability matrix, complementing the resolvent analysis for fluid flows. The right-singular vectors, referred to as the broadcast modes, give insights into the sensitive regions where introduced perturbations can be effectively spread and amplified over the entire fluid-flow network that evolves in time. We apply this analysis to a two-dimensional decaying isotropic turbulence. The broadcast mode reveals that vortex dipoles are important structures in spreading perturbations. By perturbing the flow with the principal broadcast mode, we demonstrate the utility of the insights gained from the present analysis for effectively modifying the evolution of turbulent flows. The current network-inspired work presents a novel use of network analysis to guide flow control efforts, in particular for time-varying base flows.
7 citations
TL;DR: In this article, a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions is described, including subgraph centrality and Katz centrality.
Abstract: We describe a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag–Leffler functions. This overarching theory includes as special cases well known centrality measures like subgraph centrality and Katz centrality. The indices we introduce are parametrized by two numbers; by letting these vary, we show that Mittag–Leffler centralities interpolate between degree and eigenvector centrality, as well as between resolvent-based and exponential-based indices. We further discuss modelling and computational issues, and provide guidelines on parameter 10 selection. The theory is then extended to the case of networks that evolve over time. Numerical experiments on synthetic and real-world networks are provided.
6 citations
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
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TL;DR: In this article, a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions is presented, which includes well-known centrality measures like subgraph centrality and Katz centrality.
Abstract: We describe a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions. This overarching theory includes as special cases well-known centrality measures like subgraph centrality and Katz centrality. The indices we introduce are parametrized by two numbers; by letting these vary, we show that Mittag-Leffler centralities interpolate between degree and eigenvector centrality, as well as between resolvent-based and exponential-based indices. We further discuss modeling and computational issues, and provide guidelines on parameter selection. The theory is then extended to the case of networks that evolve over time. Numerical experiments on synthetic and real-world networks are provided.
2 citations
15 Sep 2021
TL;DR: In this paper, the authors used the Katz centrality and Neumann series to identify the station importance of Taipei metro system, and the top-K important stations were demonstrated to obtain the same results as the conventional MI method.
Abstract: In this paper, the Katz centrality and Neumann series are used to identify the station importance of Taipei metro system. First, node importance of complex network is computed by the Katz centrality whose solution needs to solve the matrix inversion (MI). To get a MI free computation method, the truncated Neumann series expansion is then employed to approximate the MI. Next, a polynomial graph filtering implementation structure is presented to realize the proposed computation method. Finally, the station importance of Taipei metro system is identified by the conventional MI method and the proposed method. The top-K important stations are demonstrated to show both methods obtain the same results, so the proposed approximation method performs well.
2 citations
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TL;DR: In this article, the authors proposed a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (Interval-Weighted Networks).
Abstract: Centrality measures are used in network science to evaluate the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality, and betweenness centrality have solely assumed the edge weights to be constants. This paper proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (Interval-Weighted Networks -- IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.
1 citations
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TL;DR: In this paper, the influence maximization problem is formulated as a mixed integer nonlinear programming problem and adopted derivative-free methods, and a customised direct search method is proposed for the proposed diffusion model, with local convergence.
Abstract: Information diffusion in social networks is a central theme in computational social sciences, with important theoretical and practical implications, such as the influence maximisation problem for viral marketing. Two widely adopted diffusion models are the independent cascade model where nodes adopt their behaviour from each neighbour independently, and the linear threshold model where collective effort from the whole neighbourhood is needed to influence a node. However, both models suffer from certain drawbacks, including a binary state space, where nodes are either active or not, and the absence of feedback, as nodes can not be influenced after having been activated. To address these issues, we consider a model with continuous variables that has the additional advantage of unifying the two classic models, as the extended independent cascade model and the extended linear threshold model are recovered by setting appropriate parameters. For the associated influence maximisation problem, the objective function is no longer submodular, a feature that most approximation algorithms are based on but is arguably strict in practice. Hence, we develop a framework, where we formulate the influence maximisation problem as a mixed integer nonlinear programming and adopt derivative-free methods. Furthermore, we propose a customised direct search method specifically for the proposed diffusion model, with local convergence. We also show that the problem can be exactly solved in the case of linear dynamics by selecting nodes according to their Katz centrality. We demonstrate the rich behaviour of the newly proposed diffusion model and the close-to-optimal performance of the customised direct search numerically on both synthetic and real networks.
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TL;DR: In this paper, the authors propose an axiom system for four classic feedback centralities: Eigenvector centrality, Katz centrality and PageRank, and prove that each of these four centrality measures can be uniquely characterized with a subset of their axioms.
Abstract: In recent years, the axiomatic approach to centrality measures has attracted attention in the literature. However, most papers propose a collection of axioms dedicated to one or two considered centrality measures. In result, it is hard to capture the differences and similarities between various measures. In this paper, we propose an axiom system for four classic feedback centralities: Eigenvector centrality, Katz centrality, Katz prestige and PageRank. We prove that each of these four centrality measures can be uniquely characterized with a subset of our axioms. Our system is the first one in the literature that considers all four feedback centralities.
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TL;DR: In this article, a distributed detection of central nodes in complex networks using closeness centrality is proposed, which reduces the number of messages exchanged to determine the centrality of the remaining nodes.
Abstract: This paper is concerned with distributed detection of central nodes in complex networks using closeness centrality. Closeness centrality plays an essential role in network analysis. Evaluating closeness centrality exactly requires complete knowledge of the network; for large networks, this may be inefficient, so closeness centrality should be approximated. Distributed tasks such as leader election can make effective use of centrality information for highly central nodes, but complete network information is not locally available. This paper refines a distributed centrality computation algorithm by You et al. [24] by pruning nodes which are almost certainly not most central. For example, in a large network, leave nodes can not play a central role. This leads to a reduction in the number of messages exchanged to determine the centrality of the remaining nodes. Our results show that our approach reduces the number of messages for networks which contain many prunable nodes. Our results also show that reducing the number of messages may
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TL;DR: In this paper, the Shannon entropy of the distribution at time t of a continuous-time random walk is used to rank nodes as a function of the time t, which acts as a parameter and defines the scale of the network.
Abstract: In this article we introduce an entropy-based, scale-dependent centrality that is evaluated as the Shannon entropy of the distribution at time t of a continuous-time random walk. It ranks nodes as a function of the time t, which acts as a parameter and defines the scale of the network. It is able capture well-known centralities such as degree, eigenvector and closeness depending on the range of t. We compare it with the broad class of total $f$-communicability centralities, of which both Katz centrality and total communicability are particular cases.
TL;DR: A useful tool based on hedging networks that allows portfolio managers to allocate capital so as to build portfolios with low risk and it is shown that these portfolios achieve lower variance than other classical portfolio strategies, both in-sample and out-of-sample.
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TL;DR: In this article, the authors study walk-based centrality measures for time-ordered network sequences and propose a framework for capturing dynamic walk combinatorics when either or both is disallowed.
Abstract: We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performed entirely at the node level. We then consider two distinct types of backtracking and develop a framework for capturing dynamic walk combinatorics when either or both is disallowed.
TL;DR: Two algorithms are used in this work to find the influential node in social network with maximum influence spread and minimal time, namely Trilateral Statistical Node Extraction algorithm and Katz Centrality Least Angle Influence Node Tracing algorithm, respectively.
Abstract: With the epidemic growth of Online Social Networks (OSNs), a large scale research on information dissemination in OSNs has been made an appearance in contemporary years. One of the essential researches is Influence Maximization. Most research adopts community structure, greedy stage, and centrality measures, to identify the influence node set. However, the time consumed in analyzing the influence node set for edge server placement, service migration and service recommendation is ignored in terms of propagation delay. Considering the above analysis, we concentrate on the issue of time-sensitive influence maximization and maximize the targeted influence spread. To solve the problem, we propose a method called, Trilateral Spearman Katz Centrality-based Least Angle Regression for influential node tracing in social network. Besides, two algorithms are used in our work to find the influential node in social network with maximum influence spread and minimal time, namely Trilateral Statistical Node Extraction algorithm and Katz Centrality Least Angle Influence Node Tracing algorithm, respectively. Extensive experiments on The Telecom dataset demonstrate the efficiency and influence performance of the proposed algorithms on evaluation metrics, namely, sensitivity, specificity, accuracy, time and influence spread.