Network compression with configuration models and the minimum description length.

Area of Science:

• Network Science
• Statistical Modeling
• Data Analysis

Background:

• Random network models are crucial for analyzing network data.
• The configuration model, which constrains networks by degree distribution, is widely used but often chosen without statistical validation.
• Evaluating network model quality requires assessing information requirements and generative accuracy.

Purpose of the Study:

• To evaluate and compare different configuration model variants for network representation.
• To apply the minimum description length principle for statistically selecting the best model.
• To determine which configuration model best represents diverse real-world networks.

Main Methods:

• Calculated the size of network ensembles for various configuration models, including those with degree correlations and centrality layers.
• Applied the minimum description length principle as a model selection criterion.
• Analyzed a dataset of over 100 networks from diverse domains.

Main Results:

• The classic configuration model is preferred for networks with an average degree greater than 10.
• A layered configuration model, incorporating centrality metrics, provides the most compact representation for most sparse networks.
• Model selection varied based on network characteristics like average degree and sparsity.

Conclusions:

• The choice of configuration model significantly impacts network representation quality.
• Statistical model selection, using principles like minimum description length, is essential for accurate network analysis.
• Different network structures necessitate different modeling approaches for optimal representation.