Sample-to-sample fluctuations in real-network ensembles

Area of Science:

• Network Science
• Complex Systems
• Statistical Physics

Background:

• Ensemble averages are commonly used to model networks, assuming typicality within the ensemble.
• Previous studies indicated this assumption holds for uncorrelated networks with minimum degree ≥ 3.
• Real-world networks often exhibit structural correlations and possess low-degree nodes.

Purpose of the Study:

• To investigate the distribution of dynamically important eigenvalues in real-world networks.
• To identify the structural features responsible for deviations from typical ensemble behavior.
• To assess the influence of low-degree nodes and community structures on network dynamics.

Main Methods:

• Analysis of network eigenvalues in real-world network structures.
• Comparison of ensemble eigenvalue distributions with those of actual networks.
• Identification of structural correlations, particularly low-degree nodes (degree ≤ 3) and communities.

Main Results:

• The ensemble distribution of dynamically important eigenvalues in real networks is often broad, multimodal, and deviates significantly from the actual network eigenvalue.
• Low-degree nodes (degree ≤ 3) and network communities are identified as key drivers of these structured eigenvalue distributions.
• These structural features lead to eigenvalue distributions that are not bell-shaped.

Conclusions:

• Ensemble-based network modeling may not accurately represent the dynamics of real-world networks due to structural complexities.
• Low-degree nodes and community structures play a more critical role in collective network dynamics than previously understood.
• Future network modeling should account for the specific structural properties of real-world networks, especially the influence of low-degree nodes.