Measuring topological descriptors of complex networks under uncertainty

Area of Science:

• Network Science
• Complex Systems Analysis
• Statistical Inference

Background:

• Characterizing complex systems requires understanding network structure.
• Traditional methods necessitate full network reconstruction to compute topological descriptors.
• Inferring network structure from observed dynamics introduces uncertainty in descriptors.

Purpose of the Study:

• To develop a methodological framework for evaluating uncertainty in network topological descriptors.
• To replace point estimates of descriptors with probability distributions.
• To provide a method for transforming discriminating statistics into edge probabilities.

Main Methods:

• Proposed a theoretical framework to represent topological descriptors as probability distributions.
• Developed a process to convert discriminating statistics (e.g., correlations) into edge probabilities (πij).
• Validated the framework using numerical experiments on synthetic and real-world networks.

Main Results:

• The framework successfully evaluates uncertainty in topological descriptors, even at the single-node level.
• Theoretical predictions align with numerical experiment outcomes.
• Provided a grounded method to derive edge probabilities from statistical measures.

Conclusions:

• The developed framework offers a robust approach for analyzing network descriptors when connectivity is statistically inferred.
• Enables more accurate interpretation of centrality, clustering, and community structures.
• Facilitates network analysis in scenarios with incomplete or inferred connectivity data.