Percolation of networks with directed dependency links
Dunbiao Niu1,2, Xin Yuan3, Minhui Du1
1School of Data and Computer Science, Sun Yat-sen University, Guangzhou 510006, China.
Physical Review. E
|May 14, 2016
Summary
The self-consistent probabilistic approach reveals that network properties, like critical points in phase transitions, depend on node dependencies. Key parameters, such as the proportion of independent nodes, govern these network behaviors.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Percolation theory is crucial for understanding network robustness.
- Interdependent and multiplex networks exhibit complex behaviors.
- Directed dependency links introduce unique challenges in network analysis.
Purpose of the Study:
- To investigate the impact of directed dependency links on network criticality.
- To apply the self-consistent probabilistic approach to networks with mixed link types.
- To identify key network parameters governing phase transitions.
Main Methods:
- Utilizing a self-consistent probabilistic approach.
- Analyzing networks with both undirected connectivity and directed dependency links.
- Illustrating findings with Erdős-Rényi random networks.
Main Results:
- The critical point of second-order phase transitions is determined by the proportion of nodes with no dependencies.
- The triple point and transition boundaries are governed by nodes with at most one dependency.
- Specific network parameters dictate crucial phase transition properties.
Conclusions:
- A few key parameters can determine important properties of phase transitions in multiplex networks.
- The self-consistent probabilistic approach simplifies the study of complex network percolation.
- Directed dependency links significantly influence network criticality and phase transition behavior.
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