Inferring general relations between network characteristics from specific network ensembles.

Area of Science:

• Network Science
• Computational Biology
• Statistical Physics

Background:

• Complex systems are often modeled using various network topologies.
• Existing models focus on replicating specific statistical features but lack generalizability.
• The extrapolation of findings from one network class to real-world systems is rarely assessed.

Purpose of the Study:

• To compare network models for their ability to generate structurally variable networks.
• To identify statistical constraints imposed by network construction schemes.
• To determine generic statistical laws applicable across different network classes.

Main Methods:

• Comparison of classical and recent network models.
• Analysis of statistical constraints inherent in network generation processes.
• Development of regression models trained on high-generalization networks.
• Validation using diverse real-world network datasets (neuronal, metabolic, lexical).

Main Results:

• Identified network models with high structural variability.
• Discovered generic, model-independent statistical dependencies between network characteristics.
• Demonstrated that global network features can be inferred from local properties.
• Confirmed and extended findings on neural network synchronization.
• Validated the approach on C. elegans neuronal, R. prowazekii metabolic, and Roget's Thesaurus synonym networks.

Conclusions:

• Generic statistical laws govern complex networks, independent of specific models.
• Regression models can effectively infer global network properties from local data.
• The proposed method is valuable for analyzing large, undersampled networks, such as the human brain's neural networks.
• Real-world networks exhibit statistical relationships consistent with the derived models.