Local paths to global coherence: cutting networks down to size.

Area of Science:

• Complex Systems Science
• Network Science
• Computational Neuroscience

Background:

• Understanding the relationship between network structure and dynamics is crucial in various scientific fields.
• Global network dynamics, such as activity coherence, are often difficult to predict from local network properties.
• Existing methods struggle to account for the impact of connectivity heterogeneity on network behavior.

Purpose of the Study:

• To investigate how network connectivity impacts overall network dynamics and activity coherence.
• To establish a predictive link between local network structure and global network dynamics.
• To develop methods that account for connectivity heterogeneity and generalize the analysis to higher-order dynamics.

Main Methods:

• Characterization of local network structure using "motif cumulants," measuring deviations from probabilistic models.
• Development of a combinatorial formulation for motif cumulants, linking them to probability theory.
• Introduction of a network-partitioning method to mitigate the effects of connectivity heterogeneity.
• Generalization of dynamical coherence analysis to arbitrary orders (e.g., triplet correlations).

Main Results:

• Global network activity coherence can be predicted from local network structure (motif cumulants).
• Connectivity heterogeneity significantly affects the architecture-dynamics link, but the partitioning method recovers this relationship.
• Higher-order dynamical correlations (beyond pairwise) are influenced by a limited set of specific network motifs.

Conclusions:

• Local network architecture, quantified by motif cumulants, is a strong predictor of global network dynamics.
• A novel network-partitioning approach effectively handles connectivity heterogeneity, revealing robust architecture-dynamics relationships.
• The study provides a generalized framework for analyzing network dynamics at multiple orders, highlighting the critical role of specific motifs.