Geometric Correlations Mitigate the Extreme Vulnerability of Multiplex Networks against Targeted Attacks

Kleineberg, Kaj-Kolja; Buzna, Ľuboš; Papadopoulos, Fragkiskos; Boguñá, Marián; Serrano, M. Ángeles

doi:10.1103/physrevlett.118.218301

Cited by 46 publications

(45 citation statements)

References 25 publications

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“…However, in reality, interactions take place in different domains, such as business, circles of friends, family etc. Such interactions can be captured by multiplex networks, which are systems comprised of several network layers, where the same set of individuals are present [17][18][19][20][21]. The impact of multiplexity on the outcome of evolutionary games is of high importance for the emergence and stability of cooperation in real systems and has recently attracted a lot of attention [22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we show that the interplay between evolutionary dynamics and the structural organization of the multiplex can have dramatic consequences for the effectiveness of incentive schemes. In particular, if the degree of nodes (which may abstract their importance) is correlated among different domains, which is the case in most real multiplexes [19][20][21][35][36][37], the evolutionary dynamics can become enslaved by the topology (topological enslavement). This means that the hubs may dominate the game dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Topological enslavement in evolutionary games on correlated multiplex networks

Kleineberg¹,

Helbing²

2018

New J. Phys.

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Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoners dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner's dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions. OPEN ACCESS RECEIVED

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological enslavement in evolutionary games on correlated multiplex networks

Kleineberg¹,

Helbing²

2018

New J. Phys.

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“…As an illustration, we embedded several real-world complex networks from different domains whose degree distributions include clean scale-free, heavy-tailed, and arbitrary distributions. More specifically, the networks under study are: the world airport network 14 , the neural network of the visual cortex of the Drosophila Melanogaster at the neuron level [31], the neural network of the C. Elegans worm [32], a human connectome [33,34], the metabolic network of the bacterium E. Coli [15,35], the world trade web [16], a US commute network [36], a cargo ships network [37], a US commodities network [36], and the Internet at the Autonomous Systems level [10].…”

Section: Embedding Of Real Networkmentioning

confidence: 99%

“…Network geometry is also able to explain in a very natural way other nontrivial properties, like self-similarity [1,4] and community structure [5][6][7], their navigability properties [8][9][10], and is the basis for the definition of a renormalization group in complex networks [11]. The geometric approach has also been successfully extended to weighted networks [12] and multiplexes [13,14].…”

Section: Introductionmentioning

confidence: 99%

Mercator: uncovering faithful hyperbolic embeddings of complex networks

et al. 2019

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We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the popularity× similarity   1 2 static geometric network model, which can accommodate arbitrary degree distributions and reproduces many pivotal properties of real networks, including self-similarity patterns. The algorithm mixes machine learning and maximum likelihood (ML) approaches to infer the coordinates of the nodes in the underlying hyperbolic disk with the best matching between the observed network topology and the geometric model. In its fast mode, Mercator uses a model-adjusted machine learning technique performing dimensional reduction to produce a fast and accurate map, whose quality already outperforms other embedding algorithms in the literature. In the refined Mercator mode, the fast mode embedding result is taken as an initial condition in a ML estimation, which significantly improves the quality of the final embedding. Apart from its accuracy as an embedding tool, Mercator has the clear advantage of systematically inferring not only node orderings, or angular positions, but also the hidden degrees and global model parameters, and has the ability to embed networks with arbitrary degree distributions. Overall, our results suggest that mixing machine learning and ML techniques in a model-dependent framework can boost the meaningful mapping of complex networks.The code will be available at https://github.com/networkgeometry/mercator upon publication. 10 Notice that in thermodynamic limit the curvature of the circle vanishes and the model is effectively defined on  1 .

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“…On the other hand, positive values of between-layer correlations generally mitigate the abrupt nature of the transition, making the system more robust. Examples include degree-degree correlations (Reis et al, 2014), edge overlap (Cellai et al, 2013;Min et al, 2015;Radicchi, 2015;Radicchi & Bianconi, 2017;Baxter et al, 2016), clustering and spatial coordinates (Danziger et al, 2016;Kleineberg et al, 2016;Kleineberg et al, 2017).…”

Section: Introduction 5 Introductionmentioning

confidence: 99%

Discordant attributes of structural and functional connectivity in a two-layer multiplex network

Lim

Radicchi

Heuvel

et al. 2018

Preprint

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Several studies have suggested that functional connectivity (FC) is constrained by the underlying structural connectivity (SC) and mutually correlated. However, not many studies have focused on differences in the network organization of SC and FC, and on how these differences may inform us about their mutual interaction. To explore this issue, we adopt a multi-layer framework, with SC and FC, constructed using Magnetic Resonance Imaging (MRI) data from the Human Connectome Project, forming a two-layer multiplex network.In particular, we examine whether node strength assortativity within and between the SC and FC layer may confer increased robustness against structural failure. We find that, in general, SC is organized assortatively, indicating brain regions are on average connected to other brain regions with similar node strengths. On the other hand, FC shows disassortative mixing. This discrepancy is apparent also among individual resting-state networks within SC and FC. In addition, these patterns show lateralization, with disassortative mixing within FC subnetworks mainly driven from the left hemisphere. We discuss our findings in the context of robustness to structural failure, and we suggest that discordant and lateralized patterns of associativity in SC and FC may explain laterality of some neurological dysfunctions and recovery.

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Geometric Correlations Mitigate the Extreme Vulnerability of Multiplex Networks against Targeted Attacks

Cited by 46 publications

References 25 publications

Topological enslavement in evolutionary games on correlated multiplex networks

Topological enslavement in evolutionary games on correlated multiplex networks

Mercator: uncovering faithful hyperbolic embeddings of complex networks

Discordant attributes of structural and functional connectivity in a two-layer multiplex network

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