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Beyond the locally treelike approximation for percolation on real networks
Filippo Radicchi1, Claudio Castellano2
1Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, Indiana 47408, USA.
Physical Review. E
|April 15, 2016
Summary
This study introduces a new theoretical framework for site percolation on real-world networks, improving accuracy by accounting for graph loops. The method significantly enhances predictions compared to previous approximations.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Existing theories for percolation on real-world networks often use the locally treelike approximation.
- This approximation is limited due to the high frequency of short loops in real-world graphs.
Purpose of the Study:
- To develop a theoretical framework that overcomes the limitations of the locally treelike ansatz for site percolation.
- To accurately predict percolation diagrams on real-world networks.
Main Methods:
- A message passing algorithm is developed, specifically designed to discount redundant paths along triangles.
- The framework is systematically tested on 98 real-world graphs and synthetic networks.
Main Results:
- The new framework demonstrates excellent accuracy in predicting the entire percolation diagram.
- Significant improvements are observed compared to predictions from the locally treelike approximation.
- Discrepancies are attributed to loops longer than three edges, not clustering.
Conclusions:
- The proposed message passing algorithm provides a more accurate theoretical description of site percolation on networks with loops.
- The method offers a substantial advancement over previous approaches, particularly for complex network structures.
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