Random geometric graphs

Dall, Jesper; Christensen, Michael

doi:10.1103/physreve.66.016121

Cited by 454 publications

(499 citation statements)

References 37 publications

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“…Moreover, they pointed out that the mobility led the system to only two stable states (i.e., all cooperators or all defectors). In contrast, when v = 0 the graph corresponds to a random geometric graph [48], so the stabilization of a population containing a mixture of the two strategies is expected.…”

Section: The Key Role Of Mobilitymentioning

confidence: 99%

Effects of punishment in a mobile population playing the prisoner's dilemma game

Amor

Fort

2011

Phys. Rev. E

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We deal with a system of prisoner's dilemma players undergoing continuous motion in a two-dimensional plane. In contrast to previous work, we introduce altruistic punishment after the game. We find punishing only a few of the cooperator-defector interactions is enough to lead the system to a cooperative state in environments where otherwise defection would take over the population. This happens even with soft nonsocial punishment (where both cooperators and defectors punish other players, a behavior observed in many human populations). For high enough mobilities or temptations to defect, low rates of social punishment can no longer avoid the breakdown of cooperation.

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Section: The Key Role Of Mobilitymentioning

confidence: 99%

Effects of punishment in a mobile population playing the prisoner's dilemma game

Amor

Fort

2011

Phys. Rev. E

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“…22,23 While time series networks can reflect the dynamical properties of time series obtained from a complex system in a smorgasbord of different ways, pyunicorn focusses on two complementary approaches: (i) Recurrence networks, 24,25 an approach closely related to recurrence quantification analysis of recurrence plots, are random geometric graphs 26,119 representing proximity relationships (links) of state vectors (nodes) in phase space (Sec. IV A).…”

Section: Network-based Time Series Analysismentioning

confidence: 99%

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package

Donges

Heitzig

Beronov

et al. 2015

Chaos

111

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We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni-and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Network theory and nonlinear time series analysis provide powerful tools for the study of complex systems in various disciplines such as climatology, neuroscience, social science, infrastructure or economics. In the last years, combining both frameworks has yielded a wealth of new approaches for understanding and modeling the structure and dynamics of such systems based on the statistical analysis of network or uni-and multivariate time series. The pyunicorn software package (available at https://github.com/pik-copan/pyunicorn) facilitates the innovative synthesis of methods from network theory and nonlinear time series analysis in order to develop novel integrated methodologies. This paper provides an overview of the functionality provided by pyunicorn, introduces the theoretical concepts behind it and provides examples in the form of selected use cases mainly in the fields of climatology and paleoclimatology.

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“…A standard RGG can be constructed by distributing N points uniformly at random in some topological space, e.g., the two dimensional unit square, and connecting all pairs of nodes that are separated by a Euclidian distance less than a fixed threshold, R. There is an extensive literature on random geometric graphs, particularly in the context of continuum percolation (Dall and Christensen, 2002;Penrose, 2003;Barthélemy, 2011). The degree distribution of a RGG is Poisson with mean equal to N πR 2 (Dall and Christensen, 2002).…”

Section: Previous Workmentioning

confidence: 99%

“…The degree distribution of a RGG is Poisson with mean equal to N πR 2 (Dall and Christensen, 2002). The clustering coefficient of a RGG tends to 1 − 3 √ 3 4π ∼ 0.5865 for all 2-dimensional RGGs in the Euclidean space (Dall and Christensen, 2002), and their assortativity tends to the same value (Antonioni and Tomassini, 2012;Barnett et al, 2007).…”

Section: Previous Workmentioning

confidence: 99%

Contagion on Networks with Self-Organised Community Structure

Antonioni¹,

Bullock²,

Darabos³

et al. 2015

07/20/2015-07/24/2015

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Living systems are organised in space. This imposes constraints on both their structural form and, consequently, their dynamics. While artificial life research has demonstrated that embedding an adaptive system in space tends to have a significant impact on its behaviour, we do not yet have a full account of the relevance of spatiality to living self-organisation.Here, we extend the REDS model of spatial networks with self-organised community structure to include the "small world" effect. We demonstrate that REDS networks can become small worlds with the introduction of a small amount of random rewiring. We then explore how this rewiring influences two simple dynamic processes representing the contagious spread of infection or information.We show that epidemic outbreaks arise more easily and spread faster on REDS networks compared to standard random geometric graphs (RGGs). Outbreaks spread even faster on small world REDS networks (due to their shorter path lengths) but initially find it more difficult to establish themselves (due to their reduced community structure). Overall, we find that small world REDS networks, with their combination of short characteristic path length, positive assortativity, strong community structure and high clustering, are more susceptible to a range of contagion dynamics than RGGs, and that they offer a useful abstract model for studying dynamics on spatially organised living systems.

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Random geometric graphs

Cited by 454 publications

References 37 publications

Effects of punishment in a mobile population playing the prisoner's dilemma game

Effects of punishment in a mobile population playing the prisoner's dilemma game

Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package

Contagion on Networks with Self-Organised Community Structure

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Random geometric graphs

Cited by 454 publications

References 37 publications

Effects of punishment in a mobile population playing the prisoner's dilemma game

Effects of punishment in a mobile population playing the prisoner's dilemma game

Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

Contagion on Networks with Self-Organised Community Structure

Contact Info

Product

Resources

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Unified functional network and nonlinear time series analysis for complex systems science: The`pyunicorn`package