Growing networks of overlapping communities with internal structure

Area of Science:

• Social network analysis
• Complex systems science
• Statistical physics

Background:

• Understanding the structure and evolution of social networks is crucial.
• Existing models often struggle to capture both community emergence and internal dynamics.
• The concept of Dunbar's number suggests a limit on social connections.

Purpose of the Study:

• To introduce an intuitive model for growing social networks.
• To explain the emergence of community structure and internal community evolution.
• To reproduce global network statistics and predict new network properties.

Main Methods:

• Developed a model (SPA+) combining two mechanisms: internal community link evolution and structural preferential attachment (SPA).
• The first mechanism models node link establishment and new node introduction rates.
• The second mechanism generalizes preferential attachment to overlapping communities.

Main Results:

• The model reproduces key network statistics: community size, node membership, and degree distributions.
• It predicts three regimes for degree distribution in overlapping communities.
• Demonstrates strong correlations between node community membership and intra-community connections, linking to Dunbar's number.

Conclusions:

• The SPA+ model provides an intuitive framework for understanding growing social networks.
• The model successfully captures essential features of real-world complex networks.
• Findings offer insights into the interplay between individual social capacity and network structure.