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Condensation transitions in a model for a directed network with weighted links
A G Angel1, T Hanney, M R Evans
1SUPA and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, UK.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
This study introduces an exactly solvable model for network rewiring dynamics, revealing two condensation phases where link weights or node weights concentrate. This model maps to a solvable particle hopping process, enabling theoretical predictions.
Area of Science:
- Complex systems
- Network science
- Statistical physics
Background:
- Understanding the dynamics of complex networks is crucial in various scientific fields.
- Weighted and directed networks exhibit intricate rewiring behaviors that are challenging to model analytically.
- Existing models often lack exact solvability, limiting theoretical predictions.
Purpose of the Study:
- To introduce a novel, exactly solvable model for the rewiring dynamics of weighted, directed networks.
- To investigate the emergent phenomena of condensation in such network models.
- To establish a theoretical framework for predicting condensation conditions.
Main Methods:
- Development of an exactly solvable mathematical model for network rewiring.
- Utilizing computer simulations to observe network dynamics and condensation phenomena.
- Mapping the network model's dynamics to a zero-range process (ZRP) with interacting particles.
Main Results:
- The model demonstrates two distinct condensation phases: out-strength condensation onto a single link and total weight condensation into a single node.
- The mapping to the ZRP allows for detailed analysis of the network model's steady state.
- Theoretical predictions for the conditions leading to each condensation type were derived.
Conclusions:
- The introduced exactly solvable model provides significant insights into weighted, directed network rewiring.
- The mapping to the ZRP is a powerful tool for analyzing network dynamics and generalizing the model.
- The findings offer a theoretical basis for understanding and predicting condensation phenomena in complex networks.
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