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Diversity of information pathways drives sparsity in real-world networks

Nature Physics volume 20, pages 512–519 (2024)Cite this article

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Abstract

Complex systems must respond to external perturbations and, at the same time, internally distribute information to coordinate their components. Although networked backbones help with the latter, they limit the components’ individual degrees of freedom and reduce their collective dynamical range. Here we show that real-world networks balance the loss of response diversity with gain in information flow. Encoding network states as density matrices, we demonstrate that such a trade-off mathematically resembles the thermodynamic efficiency characterized by heat and work in physical systems, providing a variational principle to macroscopically explain the sparsity and empirical scaling law observed in hundreds of real-world networks across multiple domains, both analytically and numerically. We show that the emergence of topological features such as modularity, small-worldness and heterogeneity agrees with maximizing the trade-off between information exchange and response diversity from middle to large temporal scales. Our results suggest that the emergence of some of the most prevalent topological features of real-world networks might have a thermodynamic origin.

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Fig. 1: Response diversity and information propagation.
Fig. 2: Effect of topological features on η.
Fig. 3: Scaling in empirical networks.
Fig. 4: Biological networks compared with null models.
Fig. 5: Non-biological networks compared with null models.

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Data availability

The data necessary to reproduce the results of this work are available in Supplementary Data 1.

Code availability

The code necessary to reproduce the results of this work is available in Supplementary Code 1.

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Acknowledgements

M.D.D. acknowledges partial financial support from the Human Frontier Science Program Organization (HFSP ref. RGY0064/2022), from the University of Padua (PRD-BIRD 2022) and from the EU funding within the MUR PNRR ‘National Center for HPC, BIG DATA AND QUANTUM COMPUTING’ (project no. CN00000013 CN1).

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Authors and Affiliations

  1. Department of Physics and Astronomy ‘Galileo Galilei’, University of Padua, Padova, Italy

    Arsham Ghavasieh & Manlio De Domenico

  2. Fondazione Bruno Kessler, Povo, Italy

    Arsham Ghavasieh

  3. Department of Physics, University of Trento, Povo, Italy

    Arsham Ghavasieh

  4. Padua Center for Network Medicine, University of Padua, Padova, Italy

    Manlio De Domenico

  5. Istituto Nazionale di Fisica Nucleare, Padova, Italy

    Manlio De Domenico

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  1. Arsham Ghavasieh
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A.G. and M.D.D. designed the study, performed the theoretical analysis and wrote the manuscript. A.G. performed the numerical experiments.

Corresponding authors

Correspondence to Arsham Ghavasieh or Manlio De Domenico.

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Nature Physics thanks Baruch Barzel and Roger Guimerà for their contribution to the peer review of this work.

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Supplementary information

Supplementary Code 1

The necessary code to reproduce the results of this work.

Supplementary Data 1

Node and link numbers of the empirical networks relevant for the allometric scaling analysis.

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Ghavasieh, A., De Domenico, M. Diversity of information pathways drives sparsity in real-world networks. Nat. Phys. 20, 512–519 (2024). https://doi.org/10.1038/s41567-023-02330-x

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