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Characterizing the dynamics of unlabeled temporal networks.

Annalisa Caligiuri1, Tobias Galla1, Lucas Lacasa1

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This study introduces methods to analyze temporal networks without node labels, using graph invariants to understand network dynamics. The findings enable characterization of unlabeled network trajectories and their dynamical properties.

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Area of Science:

  • Complex Systems
  • Network Science
  • Dynamical Systems

Background:

  • Temporal networks, representing systems evolving over time, are crucial for understanding complex systems.
  • Analyzing temporal networks with unlabeled nodes is challenging due to the lack of node correspondence across time snapshots.
  • Existing methods for dynamical systems analysis often require labeled nodes, limiting their application to unlabeled temporal networks.

Purpose of the Study:

  • To extend dynamical system concepts and network-dynamical quantifiers to temporal networks with unlabeled nodes.
  • To develop methods for characterizing the dynamical properties of unlabeled temporal network trajectories.
  • To address the challenge of analyzing network evolution when node identities are not trackable over time.

Main Methods:

  • Exploiting graph invariants to adapt existing network-dynamical quantifiers.
  • Focusing on autocorrelation functions and sensitive dependence on initial conditions.
  • Utilizing synthetic graph dynamics and empirical temporal networks with removed node labels for validation.

Main Results:

  • Successfully extended network-dynamical quantifiers (autocorrelation, sensitive dependence on initial conditions) to unlabeled temporal networks.
  • Demonstrated the capability of these measures to recover and estimate dynamical fingerprints even without node labels.
  • Validated the proposed methods on both synthetic and empirical unlabeled temporal network data.

Conclusions:

  • Graph invariants provide a viable approach to analyze dynamical properties of unlabeled temporal networks.
  • The developed methods offer a robust way to study network evolution in scenarios with missing node information.
  • This work opens new avenues for understanding complex systems where node tracking is infeasible or restricted.