From lines to networks.

Area of Science:

• Complex systems science
• Network theory
• Mathematical modeling

Background:

• Most spatial network models focus on node-based growth.
• Real-world networks often grow via extension and intersection of lines (e.g., subway systems, fungal mycelia).
• A gap exists in understanding networks formed by spatially extended components.

Purpose of the Study:

• Introduce a minimal model for spatial network formation based on line growth and intersection.
• Investigate the emergent architecture and scaling behaviors of these line-grown networks.
• Provide a universal paradigm beyond node-based approaches for complex systems.

Main Methods:

• Developed a model where lines grow greedily to maximize local coverage, intersecting existing structures.
• Incorporated angular continuity and geometric constraints into the line growth process.
• Analyzed emergent network architecture (core-and-branches) and scaling properties.

Main Results:

• The line-based growth model spontaneously generates a core-and-branches architecture.
• Observed non-trivial scaling behaviors, including subquadratic intersection growth.
• Identified emergent Flory exponents and fractal dimensions consistent with empirical data.
• Spatial scaling exponents correlate with point distribution heterogeneity, matching subway system data.

Conclusions:

• The proposed line-based growth model captures key organizational features of diverse real-world networks.
• Demonstrates how growth of extended elements shapes large-scale network architecture.
• Establishes a universal paradigm for understanding spatial networks beyond node-centric models.