Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Scholtes, Ingo; Wider, Nicolas; Pfitzner, René; Garas, Antonios; Tessone, Claudio J.; Schweitzer, Frank

doi:10.1038/ncomms6024

Cited by 289 publications

(317 citation statements)

References 50 publications

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“…We used the map equation framework, because it was straightforward to generalize its mathematics to second-order Markov dynamics, but the results are, in principle, universal for any method operating on the dynamics on a network 31 . The universality is manifested in the direct effect memory in network flows has on the spectral gap 40,41 . If memory favours spread across a system, the spectral gap increases and, the other way around, if memory confines flow, the spectral gap decreases.…”

Section: Resultsmentioning

confidence: 99%

Memory in network flows and its effects on spreading dynamics and community detection

et al. 2014

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Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking and spreading analysis, although it ignores a potentially important feature of the dynamics: where flow moves to may depend on where it comes from. Here we analyse pathways from different systems, and although we only observe marginal consequences for disease spreading, we show that ignoring the effects of second-order Markov dynamics has important consequences for community detection, ranking and information spreading. For example, capturing dynamics with a second-order Markov model allows us to reveal actual travel patterns in air traffic and to uncover multidisciplinary journals in scientific communication. These findings were achieved only by using more available data and making no additional assumptions, and therefore suggest that accounting for higher-order memory in network flows can help us better understand how real systems are organized and function.

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Section: Resultsmentioning

confidence: 99%

Memory in network flows and its effects on spreading dynamics and community detection

et al. 2014

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“…While we do know that real-world diffusion in social or mobility network exhibits non-Markovian patterns [12,26], those patterns sometimes favour, and sometimes reject backtracking regardless of the degree of burstiness of the process, making it clear that they cannot be entirely accounted for by the effect at play in this paper. Whether the burstiness-induced memory is an undesirable artefact of the model or a useful and economical way to generate non-Markovian walks remains to be seen.…”

Section: Discussionmentioning

confidence: 82%

“…Driven by the availability of longitudinal data of empirical networked systems, and the increased importance of temporal networks [7,8], it is only much more recently that researchers have considered how the temporal properties of a network affect diffusion. Empirical observations have shown that temporal properties of networks strongly differ from classical homogeneous Poisson processes, due to their non-stationarity [9], correlations between the activation times of network entities [10][11][12] and fat-tailed inter-event times of activations [13]. A central question is to understand the mechanisms that either accelerate or slow down the diffusion, for instance through the characteristic time for the dynamics to converge to the equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

Backtracking and Mixing Rate of Diffusion on Uncorrelated Temporal Networks

Gueuning

Lambiotte

Delvenne

2017

Entropy

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Abstract:We consider the problem of diffusion on temporal networks, where the dynamics of each edge is modelled by an independent renewal process. Despite the apparent simplicity of the model, the trajectories of a random walker exhibit non-trivial properties. Here, we quantify the walker's tendency to backtrack at each step (return where he/she comes from), as well as the resulting effect on the mixing rate of the process. As we show through empirical data, non-Poisson dynamics may significantly slow down diffusion due to backtracking, by a mechanism intrinsically different from the standard bus paradox and related temporal mechanisms. We conclude by discussing the implications of our work for the interpretation of results generated by null models of temporal networks.

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“…In that respect, it was shown how time ordering interactions, thus causality, affect the interpretation of dynamical processes: in particular, by comparing contrasting features on moderate size time aggregated networks and on their sub-structured time dependent counterparts. Scholtes et al [7], Scholtes et al [8] also showed that some community detection can be made by means of spectral clustering.…”

Section: Introductionmentioning

confidence: 99%

“…In recent times, interesting observations on the diffusion of knowledge in structuring time dependent networks have followed such a path [7,8] . In that respect, it was shown how time ordering interactions, thus causality, affect the interpretation of dynamical processes: in particular, by comparing contrasting features on moderate size time aggregated networks and on their sub-structured time dependent counterparts.…”

Section: Introductionmentioning

confidence: 99%

Slow-down or speed-up of inter- and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network

Ausloos

2015

Front. Phys.

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Citation:Ausloos M (2015) Slow-down or speed-up of inter-and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network. Front. Phys. 3:43. doi: 10.3389/fphy.2015.00043 Slow-down or speed-up of inter-and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP), on one hand, and the Darwinian Evolution Defenders (DED), on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix built from time ordered selected quotations of agents, whence for inter-and intra-communities. The network is intrinsically directed and not necessarily reciprocal. Thus, the adjacency matrices have complex eigenvalues; the eigenvectors present complex components. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with non-Markovian contact sequences, can be made by comparing the real time dependent (directed) network to its counterpart, the time aggregated (undirected) network, -which has real eigenvalues. In order to do so, small world networks which both contain an odd number of nodes are studied and compared to similar networks with an even number of nodes. It is found that (i) the diffusion of knowledge is more difficult on the largest networks; (ii) the network size influences the slowing-down or speeding-up diffusion process. Interestingly, it is observed that (iii) the diffusion of knowledge is slower in IDP and faster in DED communities. It is suggested that the finding can be "rationalized," if some "scientific quality" and "publication habit" is attributed to the agents, as common sense would guess. This finding offers some opening discussion toward tying scientific knowledge to belief.

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Causality-driven slow-down and speed-up of diffusion in non-Markovian temporal networks

Cited by 289 publications

References 50 publications

Memory in network flows and its effects on spreading dynamics and community detection

Memory in network flows and its effects on spreading dynamics and community detection

Backtracking and Mixing Rate of Diffusion on Uncorrelated Temporal Networks

Slow-down or speed-up of inter- and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network

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