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Fundamental Dynamics of Popularity-Similarity Trajectories in Real Networks
Evangelos S Papaefthymiou1, Costas Iordanou1, Fragkiskos Papadopoulos1
1Department of Electrical Engineering, Computer Engineering and Informatics, Cyprus University of Technology, 3036 Limassol, Cyprus.
Physical Review Letters
|July 12, 2024
Summary
Real network dynamics are predictable, exhibiting self-similar properties and mean-reverting behavior. This suggests hidden geometric structures govern network evolution, paving the way for new mathematical theories.
Area of Science:
- Complex Systems
- Network Science
- Dynamical Systems Theory
Background:
- Real networks are complex dynamical systems with evolving structures.
- A principled mathematical theory for network dynamics is currently lacking.
- Understanding network evolution is crucial for various scientific domains.
Purpose of the Study:
- To investigate the dynamical properties of real networks.
- To identify universal behaviors in network evolution.
- To establish a mathematical framework for predicting network dynamics.
Main Methods:
- Analysis of node popularity and similarity trajectories in hyperbolic embeddings.
- Application of Hurst exponent calculations to quantify self-similarity.
- Comparison of real network dynamics with synthetic network models.
Main Results:
- Node trajectories exhibit universal self-similar properties with Hurst exponents H≪0.5.
- Network dynamics display predictable, antipersistent, or mean-reverting behavior.
- These dynamics are captured by fractional Brownian motion and linked to latent network geometry.
Conclusions:
- Real network dynamics possess predictable, subdiffusive characteristics.
- The hidden geometry of networks is fundamental to their observed dynamics.
- This study lays the groundwork for a rigorous mathematical theory of real network dynamics.
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