Estimation of global network statistics from incomplete data.

Area of Science:

• Complex networks
• Network science
• Data science

Background:

• Real-world systems (social, biological, physical, virtual) are often complex networks.
• Observing complete network data (all nodes and interactions) is frequently impossible.
• Existing methods for partial network data are limited and often yield inaccurate network statistics.

Purpose of the Study:

• To develop novel scaling methods for predicting true network statistics from partial network data.
• To enable accurate estimation of network properties like degree distribution, even with missing nodes, links, or weights.
• To provide a transparent approach applicable to diverse network analysis scenarios without assuming a network generation process.

Main Methods:

• Generation of novel scaling methods to predict network statistics.
• Validation using simulated network classes and empirical datasets.
• Subsampling experiments to assess estimation accuracy across varying data proportions.
• Application to large-scale Twitter reply networks (100 million tweets).

Main Results:

• The developed scaling methods provide accurate estimates of true network statistics from incomplete data.
• Validation confirmed the efficacy of the methods on diverse simulated and real-world networks.
• Analysis of Twitter data revealed a statistical characterization of the Twitter Interactome.
• Support for Dunbar's hypothesis regarding the threshold of active social contacts was found.

Conclusions:

• The proposed scaling methods effectively predict key network statistics from partial observations.
• These techniques offer a robust solution for analyzing complex networks with incomplete data.
• The study provides statistical insights into large-scale social networks and human social behavior thresholds.