Analytically solvable autocorrelation function for weakly correlated interevent times

Jo, Hang-Hyun

doi:10.1103/physreve.100.012306

Cited by 9 publications

(3 citation statements)

References 43 publications

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“…The upper bound of A for any P (x) is known as 1/3, implying that |ρ x | ≤ 1/3 [31]. The FGM copula has recently been used for modeling the bivariate luminosity function of galaxies [32] and bursty time series with correlated interevent times [33,34]. By plugging Eq.…”

Section: A Analysismentioning

confidence: 99%

Analytical approach to the generalized friendship paradox in networks with correlated attributes

Jo,

Lee,

Eom

2021

Preprint

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One of the interesting phenomena due to the topological heterogeneities in complex networks is the friendship paradox, stating that your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary nodal attributes, called a generalized friendship paradox (GFP). In this paper, we analyze the GFP for the networks in which the attributes of neighboring nodes are correlated with each other. The correlation structure between attributes of neighboring nodes is modeled by the Farlie-Gumbel-Morgenstern copula, enabling us to derive approximate analytical solutions of the GFP for three kinds of methods summarizing the neighborhood of the focal node, i.e., mean-based, median-based, and fraction-based methods. The analytical solutions are comparable to simulation results, while some systematic deviations between them might be attributed to the higher-order correlations between nodal attributes. These results help us get deeper insight into how various summarization methods as well as the correlation structure of nodal attributes affect the GFP behavior, hence better understand various related phenomena in complex networks.

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Section: A Analysismentioning

confidence: 99%

Analytical approach to the generalized friendship paradox in networks with correlated attributes

Jo,

Lee,

Eom

2021

Preprint

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“…As the analytical calculation of γ as a function of β is a very challenging task, one can tackle a simplified problem. For example, the effects of correlations only between two consecutive IETs on the autocorrelation function have been analytically studied to find the M -dependence of γ [39].…”

Section: Temporal Scaling Behaviorsmentioning

confidence: 99%

Bursty Time Series Analysis for Temporal Networks

Hiraoka

2019

Computational Social Sciences

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Characterizing bursty temporal interaction patterns of temporal networks is crucial to investigate the evolution of temporal networks as well as various collective dynamics taking place in them. The temporal interaction patterns have been described by a series of interaction events or event sequences, often showing non-Poissonian or bursty nature. Such bursty event sequences can be understood not only by heterogeneous interevent times (IETs) but also by correlations between IETs. The heterogeneities of IETs have been extensively studied in recent years, while the correlations between IETs are far from being fully explored. In this Chapter, we introduce various measures for bursty time series analysis, such as the IET distribution, the burstiness parameter, the memory coefficient, the bursty train sizes, and the autocorrelation function, to discuss the relation between those measures. Then we show that the correlations between IETs can affect the speed of spreading taking place in temporal networks. Finally, we discuss possible research topics regarding bursty time series analysis for temporal networks. * This is a preprint for a chapter to appear in Temporal Network Theory edited by P. Holme and J. Saramäki (https: //www.springer.com/gp/book/9783030234942).

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“…In essence the copula method enables to write a joint probability distribution function with tunable correlation between variables in a tractable form [33]. The copula method has been used in various disciplines such as finance [34], engineering [35], biology [36], astronomy [37,38], and time series analysis [39,40]. However, due to the complexity of the formalism for the GFP, the analytical solution could be obtained only approximately, e.g., by assuming a locally tree structure for the underlying network [29], implying that attributes of neighbors of the focal node are correlated with that of the focal node but not with each other.…”

Section: Introductionmentioning

confidence: 99%

Copula-based analysis of the generalized friendship paradox in clustered networks

Jo¹,

Lee²,

Eom³

2022

Preprint

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Analytically solvable autocorrelation function for weakly correlated interevent times

Cited by 9 publications

References 43 publications

Analytical approach to the generalized friendship paradox in networks with correlated attributes

Analytical approach to the generalized friendship paradox in networks with correlated attributes

Bursty Time Series Analysis for Temporal Networks

Copula-based analysis of the generalized friendship paradox in clustered networks

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