Chordless cycle filtrations for dimensionality detection in complex networks via topological data analysis

Area of Science:

• Complex systems analysis
• Network science
• Computational topology

Background:

• Many complex networks (social, biological) show hyperbolic geometry.
• Understanding latent space dimensionality is crucial for network analysis, navigation, and behavior.

Purpose of the Study:

• To introduce a data-driven method for estimating network dimensionality.
• To reveal the hidden geometric structure of complex networks.

Main Methods:

• Developed a topological data analysis weighting scheme based on chordless cycles.
• Utilized a neural network trained on synthetic graph data to estimate dimensionality.
• Combined cycle-aware filtrations, algebraic topology, and machine learning.

Main Results:

• The proposed method effectively estimates network dimensionality.
• The trained neural network model demonstrates transferability to real-world networks without retraining.
• The approach provides robust uncovering of hidden network geometry.

Conclusions:

• The combined approach offers a powerful tool for analyzing complex network geometry.
• Accurate dimensionality estimation facilitates better network modeling and low-dimensional embedding.
• This method enhances understanding of structure-function relationships in complex systems.