Maximum likelihood: extracting unbiased information from complex networks.

Area of Science:

• Network science
• Statistical modeling
• Complex systems analysis

Background:

• Parameter selection in network models is often subjective, depending on the topological properties of interest.
• Existing network models may be ill-defined or biased if parameter choices conflict with statistical principles.

Purpose of the Study:

• To introduce a statistically rigorous method for parameter selection in network models using the maximum likelihood principle.
• To develop unbiased network models and a technique for extracting hidden variables from network topology.
• To validate the proposed method using real-world data.

Main Methods:

• Application of the maximum likelihood (ML) principle for objective parameter selection in network models.
• Construction of a class of "safely unbiased" network models.
• Development of a method to infer "hidden variables" from network topological data.

Main Results:

• The ML principle identifies a unique, statistically sound parameter choice linked to specific topological features.
• Incompatibility between ML-derived and built-in parameters indicates model bias or ill-definition.
• The proposed method successfully recovered empirical gross domestic product from World Trade Web data using only topological information.

Conclusions:

• The maximum likelihood principle provides a robust framework for parameter selection in network modeling.
• Unbiased network models can be constructed, and hidden organizational variables can be extracted from topological data alone.
• This approach offers a powerful tool for analyzing complex networks and uncovering underlying structures.