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Stability of shortest paths in complex networks with random edge weights
1Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany.
Summary
Disorder in complex networks destabilizes spanning trees, causing phase transitions. Scale-free networks show the most stable transport patterns under disorder.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- Complex networks rely on spanning trees for transport.
- Edges not in the spanning tree are typically inactive.
- Disorder can activate edges and alter network structure.
Purpose of the Study:
- Investigate the impact of quenched disorder on network spanning trees.
- Analyze the stability and phase-transition behavior of spanning trees under disorder.
- Compare disorder effects across regular, small-world, and scale-free networks.
Main Methods:
- Analytic random-walk mappings.
- Numerical analysis of network properties.
- Examination of phase transitions and scaling behavior.
Main Results:
- Spanning trees are unstable to disorder, exhibiting phase-transition-like behavior.
- Continuous transitions observed in regular networks, first-order in small-world and scale-free networks.
- Scale-free networks demonstrate the most stable transport patterns.
Conclusions:
- Disorder fundamentally alters network spanning tree structure and transport.
- Network topology significantly influences the response to disorder.
- Scale-free networks offer enhanced robustness against transport disruptions.