Weighted networks as randomly reinforced urn processes

Area of Science:

• Network Science
• Statistical Analysis
• Complex Systems

Background:

• Weighted networks are crucial in various fields, but their dynamic evolution and stability are complex to analyze.
• Existing methods often struggle with dense networks or specific probability distributions.

Purpose of the Study:

• To develop a general statistical framework for analyzing the evolution of weighted networks over time.
• To introduce a method for detecting dominant edges and assessing network steady-state.
• To provide a tool applicable to dense networks, which are often computationally challenging.

Main Methods:

• Modeling weighted networks as randomly reinforced urn processes.
• Developing a statistical test to detect edge dominance and network steady-state.
• Applying the procedure to the International Trade Network.

Main Results:

• A general statistical test and procedure for network evolution analysis.
• Identification of dominant edges and assessment of network stability.
• Successful application to the International Trade Network, revealing a core of dominant edges.

Conclusions:

• The proposed method offers a robust way to study network dynamics and identify key structural properties.
• The approach is versatile, applicable across different network types and distributions.
• This work provides new insights into the structure and stability of complex networks, particularly dense ones.