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  • Letter
  • Open Access

Correlations of network trajectories

Lucas Lacasa1,*, Jorge P. Rodriguez2,†, and Victor M. Eguiluz1,‡

  • 1Institute for Cross-Disciplinary Physics and Complex Systems IFISC (CSIC-UIB), Palma de Mallorca, Spain
  • 2Instituto Mediterraneo de Estudios Avanzados IMEDEA (CSIC-UIB), 07190 Esporles, Spain

  • *lucas@ifisc.uib-csic.es
  • †jorgeprodriguezg@gmail.com
  • ‡victor@ifisc.uib-csic.es
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Phys. Rev. Research 4, L042008 – Published 14 October, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042008

Abstract

Temporal networks model how the interaction between elements in a complex system evolves over time. Just as complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in graph space, following a latent graph dynamical system. Under this paradigm, we propose a way to measure how the network pulsates and collectively fluctuates over time and space. To this aim, we extend the notion of linear correlation functions to the case of sequences of network snapshots, i.e., a network trajectory. We construct stochastic and deterministic graph dynamical systems and show that the emergent collective correlations are well captured by simple measures, and we illustrate how these patterns are revealed in empirical networks arising in different domains.

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Outline

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Phys. Rev. Research 4, L042008– Published 14 October, 2022
  • Received 31 January 2022
  • Revised 29 June 2022
  • Accepted 23 August 2022
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