Article

Diffusion on networked systems is a question of time or structure

  • Nature Communications 6, Article number: 7366 (2015)
  • doi:10.1038/ncomms8366
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Abstract

Network science investigates the architecture of complex systems to understand their functional and dynamical properties. Structural patterns such as communities shape diffusive processes on networks. However, these results hold under the strong assumption that networks are static entities where temporal aspects can be neglected. Here we propose a generalized formalism for linear dynamics on complex networks, able to incorporate statistical properties of the timings at which events occur. We show that the diffusion dynamics is affected by the network community structure and by the temporal properties of waiting times between events. We identify the main mechanism—network structure, burstiness or fat tails of waiting times—determining the relaxation times of stochastic processes on temporal networks, in the absence of temporal–structure correlations. We identify situations when fine-scale structure can be discarded from the description of the dynamics or, conversely, when a fully detailed model is required due to temporal heterogeneities.

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Acknowledgements

We thank Michael Schaub for carefully reading the manuscript. J.C.D. and R.L. thank financial support of IAP DYSCO and ARC ‘Mining and Optimization of Big Data Models’. R.L. acknowledges support from FNRS and from FP7 project ‘Optimizr’. L.E.C.R. is an FNRS chargé de recherches and thanks VR for financial support.

Author information

Affiliations

  1. ICTEAM and CORE, University of Louvain, 4 Avenue Lemaître, Louvain-la-Neuve B-1348, Belgium

    • Jean-Charles Delvenne
  2. Department of Mathematics and naXys, University of Namur, 8 Rempart de la Vierge, Namur B-5000, Belgium

    • Renaud Lambiotte
    •  & Luis E. C. Rocha
  3. Department of Public Health Sciences, Karolinska Institutet, 18A Tomtebodavägen, Stockholm S-17177, Sweden

    • Luis E. C. Rocha

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Contributions

J.C.D., L.E.C.R. and R.L. conceived the project and wrote the manuscript. J.C.D. derived the analytical results. L.E.C.R. performed the numerical simulations and analysed the data.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Jean-Charles Delvenne.

Supplementary information

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    Supplementary Information

    Supplementary Figure 1, Supplementary Table 1, Supplementary Notes 1-3 and Supplementary References

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