Reducibility of higher-order networks from dynamics

Area of Science:

• Complex Systems Science
• Network Science
• Information Theory

Background:

• Complex systems exhibit both pairwise and higher-order interactions, crucial for collective phenomena.
• Higher-order network models offer superior description but increase complexity and computational cost.
• A quantitative method is needed to justify higher-order modeling versus pairwise approaches.

Purpose of the Study:

• To develop a quantitative framework for assessing the necessity of higher-order interactions in complex systems.
• To determine when higher-order network models are advantageous compared to pairwise models.
• To quantify the information preserved when reducing higher-order structures to lower-order ones.

Main Methods:

• An information-theoretic framework was proposed to quantify the entropic cost and distinguishability of higher-order interactions.
• The framework assesses how network structures influence diffusion behaviors.
• Controlled randomization procedures were used to investigate reducibility, focusing on nestedness and degree heterogeneity.

Main Results:

• Empirical analyses revealed that some systems preserve essential higher-order structure.
• Other technological and biological networks showed higher-order structures collapsing to pairwise interactions.
• Nestedness and degree heterogeneity play roles in the reducibility of higher-order structures.

Conclusions:

• The proposed framework provides a method to evaluate the reducibility of complex systems' network structures.
• It helps in minimizing model dimensionality while preserving essential functional information.
• Findings guide the selection of appropriate network models for diverse empirical systems.