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Abrupt percolation in small equilibrated networks.
1Department of Chemical Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Summary
Networks can abruptly form a giant component without suppressive rules. Finite systems show instability at the percolation threshold, leading to a discontinuous transition, particularly in smaller networks.
Area of Science:
- Network science
- Statistical physics
- Graph theory
Background:
- Networks often exhibit spontaneous self-organization into a giant component.
- This phenomenon is typically observed in random graphs with rules that delay cluster formation.
Purpose of the Study:
- To investigate if suppressive rules are essential for sharp transitions at the percolation threshold.
- To explore network behavior in finite systems with a tendency to form a giant cluster.
Main Methods:
- Theoretical development for a class of equilibrated networks.
- Analysis of network transitions at the percolation threshold.
Main Results:
- Suppressing rules are not necessary for a sharp transition at the percolation threshold.
- Finite systems with aggressive giant cluster formation tendencies display instability.
- This instability results in an abrupt, discontinuous transition to a stable state.
- The discontinuous jump is more pronounced in smaller networks.
Conclusions:
- Sharp network transitions do not require suppressive rules.
- Finite system size and inherent formation tendencies drive discontinuous transitions.
- The observed effect diminishes in infinitely large systems.
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