The simpliciality of higher-order networks

Area of Science:

• Network Science
• Complex Systems Analysis
• Data Modeling

Background:

• Higher-order networks model interactions involving more than two entities.
• Existing models either ignore inclusion or assume perfect/complete inclusion.
• A nuanced approach is needed to assess inclusion in empirical systems.

Purpose of the Study:

• To introduce and define "simpliciality" as a measure of inclusion in higher-order networks.
• To analyze the distribution of simpliciality in real-world complex systems.
• To evaluate the ability of current generative models to capture network inclusion structures.

Main Methods:

• Development of the concept of simpliciality and associated quantitative measures.
• Empirical analysis of inclusion structures in various higher-order network datasets.
• Assessment of generative models against observed simpliciality distributions.

Main Results:

• Empirically observed higher-order networks rarely exhibit perfect or absent inclusion.
• Real-world systems typically display intermediate levels of simpliciality.
• Current generative models fail to accurately replicate the inclusion structures of these datasets.

Conclusions:

• The simpliciality spectrum provides a more realistic framework for higher-order network analysis.
• Existing modeling approaches are insufficient for capturing nuanced inclusion patterns.
• Findings necessitate the development of novel generative models for higher-order networks.