Dimension matters when modeling network communities in hyperbolic spaces.

Area of Science:

• Network Science
• Complex Systems
• Data Science

Background:

• Random hyperbolic graphs explain real-world network properties like clustering and navigability.
• These networks are found in diverse systems such as the internet, transportation, and biological networks.
• Hyperbolic models can generate community structures, a key feature of real networks.

Purpose of the Study:

• To investigate the impact of latent space dimensionality on hyperbolic network models.
• To demonstrate how dimensionality affects the representation of clustered networked data.
• To improve the generation of realistic and diverse community structures in hyperbolic network models.

Main Methods:

• Analysis of random hyperbolic graph models with varying latent space dimensions.
• Comparison of connection probability restrictions based on node similarity across different dimensionalities.
• Evaluation of community structure generation in lowest-dimensional versus higher-dimensional models.

Main Results:

• A qualitative difference exists between lowest-dimensional and higher-dimensional hyperbolic models regarding similarity-based connection probabilities.
• Higher dimensions increase the number of nearest neighbors for angular clusters, which represent communities.
• Even a small increase in dimensionality significantly enhances the realism and diversity of generated community structures.

Conclusions:

• Latent space dimensionality is a critical, often overlooked, factor in hyperbolic network modeling.
• Adjusting dimensionality offers a powerful mechanism to generate more accurate and varied community structures.
• This finding unifies network interpretation across diverse systems by improving community detection in hyperbolic spaces.