Networks with side branching in biology

Area of Science:

• Network theory
• Fractal geometry
• Biological systems

Background:

• Branching networks are prevalent in biology (plants, cardiovascular, bronchial).
• Many biological networks exhibit self-similarity and fractal scaling.
• Understanding side-branching patterns is crucial for network analysis.

Purpose of the Study:

• Introduce the Tokunaga taxonomy for side branching.
• Analyze deterministic and stochastic branching networks.
• Explore the universality of side-branching statistics in natural and artificial systems.

Main Methods:

• Developed the Tokunaga taxonomy and parameterization for self-similar side-branching.
• Examined deterministic branching networks with identical fractal dimensions but different side-branching parameters.
• Analyzed stochastic branching in leaf vein structures, river networks, and diffusion-limited aggregation (DLA) clusters.

Main Results:

• Deterministic networks with the same fractal dimension can possess distinct side-branching parameters.
• Leaf vein networks and river networks share nearly identical side-branching statistics.
• DLA clusters also exhibit Tokunaga side-branching statistics, suggesting universal formation principles.

Conclusions:

• The Tokunaga taxonomy provides a framework for quantifying side-branching in complex networks.
• Similar side-branching statistics in diverse systems (leaves, rivers, DLA) point to common underlying formation mechanisms.
• The model shows good agreement with the allometric scaling of metabolic rate and mass, supporting its applicability to biological systems.