Can recurrence networks show small-world property?

Jacob, Rinku; Harikrishnan, K. P.; Misra, Ranjeev; Ambika, G.

doi:10.1016/j.physleta.2016.06.038

Cited by 10 publications

(5 citation statements)

References 41 publications

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“…To our best knowledge, a similar crossover behavior has not been described in ES based climate networks before, but was reported for the ( networks established based on classical Pearson correlation [22]. Future work should further address this kind of transition behavior in network properties when increasing the density of connections, which has also been reported in other types of spatial networks [71][72][73][74] and could be related to a change in the structural complexity of the investigated network structures [21].…”

Section: Node Degreesupporting

confidence: 76%

Spatial organization of connectivity in functional climate networks describing event synchrony of heavy precipitation

Wolf

Donner

2021

Eur. Phys. J. Spec. Top.

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In the past years, there has been an increasing number of applications of functional climate networks to studying the spatio-temporal organization of heavy rainfall events or similar types of extreme behavior in some climate variable of interest. Nearly all existing studies have employed the concept of event synchronization (ES) to statistically measure similarity in the timing of events at different grid points. Recently, it has been pointed out that this measure can however lead to biases in the presence of events that are heavily clustered in time. Here, we present an analysis of the effects of event declustering on the resulting functional climate network properties describing spatio-temporal patterns of heavy rainfall events during the South American monsoon season based on ES and a conceptually similar method, event coincidence analysis (ECA). As examples for widely employed local (per-node) network characteristics of different type, we study the degree, local clustering coefficient and average link distance patterns, as well as their mutual interdependency, for three different values of the link density. Our results demonstrate that the link density can markedly affect the resulting spatial patterns. Specifically, we find the qualitative inversion of the degree pattern with rising link density in one of the studied settings. To our best knowledge, such crossover behavior has not been described before in event synchrony based networks. In addition, declustering relieves differences between ES and ECA based network properties in some measures while not in others. This underlines the need for a careful choice of the methodological settings in functional climate network studies of extreme events and associated interpretation of the obtained results, especially when higher-order network properties are considered.

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Section: Node Degreesupporting

confidence: 76%

Spatial organization of connectivity in functional climate networks describing event synchrony of heavy precipitation

Wolf

Donner

2021

Eur. Phys. J. Spec. Top.

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“…If ε is too small, the volume of the neighborhood will be small and therefore there will be almost no recurrence points and the information incorporated in the network will be insufficient. On the other hand, if ε is too large we observe a general qualitative change in the network topology (Jacob, Harikrishnan, Misra, & Ambika, 2016), namely, each node will behave like a hub, leading to an excess of recurring points and misleading information. Donner et al (2010) and Donner, Small, et al (2011) studied properties of ε-recurrence networks at three different scales, namely local, intermediate, and global on several paradigmatic systems: Hénon map, Bernoulli map, Lorenz system, and Rössler system.…”

Section: Adaptive Nearest Neighbor Networkmentioning

confidence: 96%

Section: Mapping Univariate Time Series Into Complex Networkmentioning

confidence: 99%

Time series analysis via network science: Concepts and algorithms

Silva

Ribeiro

et al. 2021

WIREs Data Min & Knowl

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There is nowadays a constant flux of data being generated and collected in all types of real world systems. These data sets are often indexed by time, space, or both requiring appropriate approaches to analyze the data. In univariate settings, time series analysis is a mature field. However, in multivariate contexts, time series analysis still presents many limitations. In order to address these issues, the last decade has brought approaches based on network science. These methods involve transforming an initial time series data set into one or more networks, which can be analyzed in depth to provide insight into the original time series. This review provides a comprehensive overview of existing mapping methods for transforming time series into networks for a wide audience of researchers and practitioners in machine learning, data mining, and time series. Our main contribution is a structured review of existing methodologies, identifying their main characteristics, and their differences. We describe the main conceptual approaches, provide authoritative references and give insight into their advantages and limitations in a unified way and language. We first describe the case of univariate time series, which can be mapped to single layer networks, and we divide the current mappings based on the underlying concept: visibility, transition, and proximity. We then proceed with multivariate time series discussing both single layer and multiple layer approaches. Although still very recent, this research area has much potential and with this survey we intend to pave the way for future research on the topic. This article is categorized under: Fundamental Concepts of Data and Knowledge > Data Concepts Fundamental Concepts of Data and Knowledge > Knowledge Representation

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“…Beyond this, our framework might also be applicable to networks constructed from non-pairwise interdependencies that are investigated in, e.g, causal effect networks [74,85,86]. The assessment of statistical complexity could help to more objectively choose thresholds for the construction of such networks and complements existing approaches based on, e.g., the assessment of the recurrence network's percolation threshold [76,87,88].…”

Section: Threshold-based Networkmentioning

confidence: 99%

Mapping and discrimination of networks in the complexity-entropy plane

et al. 2017

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Complex networks are usually characterized in terms of their topological, spatial, or informationtheoretic properties and combinations of the associated metrics are used to discriminate networks into different classes or categories. However, even with the present variety of characteristics at hand it still remains a subject of current research to appropriately quantify a network's complexity and correspondingly discriminate between different types of complex networks, like infrastructure or social networks, on such a basis. Here, we explore the possibility to classify complex networks by means of a statistical complexity measure that has formerly been successfully applied to distinguish different types of chaotic and stochastic time series. It is composed of a network's averaged pernode entropic measure characterizing the network's information content and the associated JensonShannon divergence as a measure of disequilibrium. We study 29 real world networks and show that networks of the same category tend to cluster in distinct areas of the resulting complexity-entropy plane. We demonstrate that within our framework, connectome networks exhibit among the highest complexity while, e.g, transportation and infrastructure networks display significantly lower values. Furthermore, we demonstrate the utility of our framework by applying it to families of random scale-free and Watts-Strogatz model networks. We then show in a second application that the proposed framework is useful to objectively construct threshold-based networks, such as functional climate networks or recurrence networks, by choosing the threshold such that the statistical network complexity is maximized.

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Can recurrence networks show small-world property?

Cited by 10 publications

References 41 publications

Spatial organization of connectivity in functional climate networks describing event synchrony of heavy precipitation

Spatial organization of connectivity in functional climate networks describing event synchrony of heavy precipitation

Time series analysis via network science: Concepts and algorithms

Mapping and discrimination of networks in the complexity-entropy plane

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