The Fitness-Corrected Block Model, or how to create maximum-entropy data-driven spatial social networks

Area of Science:

• Network science
• Statistical modeling
• Social network analysis

Background:

• Network models are crucial for understanding empirical patterns and generating synthetic graphs.
• Existing models like the Degree-Corrected Block Model have limitations in adjustable density and maximum entropy properties.

Purpose of the Study:

• Introduce the Fitness-Corrected Block Model (FCBM), a novel adjustable-density variation of the Degree-Corrected Block Model.
• Demonstrate that the FCBM is a maximum entropy model.
• Derive an analytical expression for the degree distribution in sparse networks.

Main Methods:

• Developed the Fitness-Corrected Block Model (FCBM).
• Derived analytical expressions for degree distribution in the sparse network regime.
• Utilized maximum entropy principles for model construction.
• Performed simulations of a stylized urban area to validate findings.

Main Results:

• The FCBM is a maximum entropy model.
• In sparse networks, the degree distribution depends on constraints and fitness distribution.
• The sparse-regime approximation aligns with phenomenological models of social link probability based on sociability, age-group cohesion, and geographic distance.
• Simulations support the analytical findings.

Conclusions:

• The FCBM provides a powerful tool for constructing maximum entropy, data-driven spatial social networks.
• The model effectively captures the interplay of individual attributes (sociability, age) and spatial factors in network formation.
• The derived analytical results offer insights into the mechanisms driving link formation in sparse social networks.