Characterizing the dynamics of unlabeled temporal networks.

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.