Evolving networks based on birth and death process regarding the scale stationarity

Area of Science:

• Network Science
• Mathematical Modeling
• Stochastic Processes

Background:

• Scale-free networks are crucial for real-world system topology analysis.
• Traditional models assume constant node growth, leading to non-stationarity, which contradicts real-world network dynamics.
• Existing models fail to capture the dynamic nature of network evolution with both node increases and decreases.

Purpose of the Study:

• To develop novel evolving network models incorporating both vertex birth and death random processes.
• To address the non-stationarity issue in traditional network scale analysis.
• To establish a theoretical framework for stationary network scales in dynamic systems.

Main Methods:

• Modeling evolving networks using birth and death random processes, conceptualized as queuing systems.
• Deriving probabilistic expressions for stationary network scales independent of time.
• Simulating network models using various queuing systems and comparing results with theoretical predictions.

Main Results:

• The proposed models demonstrate that network scales can achieve stationarity under birth and death processes.
• A specific probabilistic expression for stationary network scale, independent of time, was deduced.
• Simulations confirmed the validity and accuracy of the developed models by matching theoretical predictions.

Conclusions:

• The introduced evolving network models effectively capture dynamic network topologies with stationary scales.
• The theoretical framework and simulations provide a robust method for analyzing and predicting network evolution.
• The model's applicability extends to simulating and predicting real-world phenomena, such as national population dynamics.