Characterising the dynamics of unlabelled temporal networks

Summary

This study explores the dynamics of unlabelled temporal networks, proposing a method to characterize their behavior using graph invariants. It introduces three pseudo-distances (degree sequence, spectral, and eigenvector centrality) to compare unlabelled graphs and analyzes their behavior in detecting chaotic and periodic dynamics.

Highlights

• The study introduces a method to analyze unlabelled temporal networks using graph invariants.
• Three pseudo-distances are proposed to compare unlabelled graphs: degree sequence, spectral, and eigenvector centrality.
• These pseudo-distances are used to detect chaotic and periodic dynamics in unlabelled network trajectories.
• The method is tested on synthetic and real-world networks, including models of periodic, correlated, and chaotic dynamics.
• Results show that the pseudo-distances can capture the dynamics of unlabelled networks, but with limitations.
• The study highlights the challenges of analyzing unlabelled networks and the need for further research.
• The proposed method has potential applications in fields where node labels are not available or are not reliable.

Key Insights

• The use of graph invariants allows for the analysis of unlabelled temporal networks, providing a way to characterize their dynamics without relying on node labels.
• The proposed pseudo-distances (degree sequence, spectral, and eigenvector centrality) are effective in detecting chaotic and periodic dynamics in unlabelled network trajectories, but their performance may vary depending on the specific network and dynamics.
• The study highlights the importance of considering the limitations of the proposed method, particularly in cases where the pseudo-distances may not capture the full complexity of the network dynamics.
• The results demonstrate the potential of the proposed method for analyzing real-world networks, such as those found in social, biological, and physical systems.
• Further research is needed to explore the applicability of the proposed method to different types of networks and dynamics, as well as to develop more robust and effective methods for analyzing unlabelled temporal networks.
• The study emphasizes the need for a deeper understanding of the relationship between labelled and unlabelled networks, and how this relationship affects our ability to analyze and characterize network dynamics.
• The proposed method has implications for fields where node labels are not available or are not reliable, providing a new approach for analyzing and understanding complex network systems.

Mindmap

Citation

Caligiuri, A., Galla, T., & Lacasa, L. (2024). Characterising the dynamics of unlabelled temporal networks (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.14864