From scale-free to Erdos-Rényi networks
Jesús Gómez-Gardeñes1, Yamir Moreno
1Instituto de Biocomputacion y Física de los Sistemas Complejos (BIFI), Universidad de Zaragoza, Spain.
Summary
We introduce a network model that bridges scale-free and Erdos-Rényi networks, revealing how structural heterogeneity influences network properties. This analysis aids in understanding transitions between network types and their impact on phenomena like percolation.
Area of Science:
- Network Science
- Statistical Physics
Background:
- Scale-free and Erdos-Rényi networks represent distinct topological classes.
- Understanding the transition and interplay between these network types is crucial for modeling complex systems.
Purpose of the Study:
- To introduce and analyze a one-parameter model interpolating between scale-free and Erdos-Rényi networks.
- To investigate the role of structural heterogeneity in network properties.
- To explore the percolation transition within this model.
Main Methods:
- Development of a one-parameter network generation model.
- Analytical calculations to derive network properties.
- Extensive numerical simulations for validation and analysis.
- Application of the model to study percolation transitions.
Main Results:
- The model successfully interpolates between scale-free and Erdos-Rényi network characteristics.
- Structural heterogeneity is shown to play a key role in network behavior.
- The study characterizes the transition between the two network classes.
Conclusions:
- The proposed model provides a flexible framework for studying network transitions.
- The findings offer insights into the impact of heterogeneity on network dynamics, particularly percolation.
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