Inference of edge correlations in multilayer networks

Area of Science:

• Network analysis
• Complex systems science
• Statistical modeling

Background:

• Multilayer networks are crucial for modeling complex systems with time-dependent or multiple interaction types.
• Community structure is a key mesoscale feature in multilayer networks, often analyzed using stochastic block models (SBMs).
• Existing SBMs often assume independent edge sampling across layers, which may not accurately reflect real-world network dynamics.

Purpose of the Study:

• To develop an advanced multilayer stochastic block model (SBM) that incorporates inter-layer edge correlations.
• To introduce a novel measure for quantifying the similarity of connectivity patterns between network layers.
• To enhance the predictive accuracy of inferring network structures and missing links in multilayer networks.

Main Methods:

• Developed a novel multilayer stochastic block model (SBM) that relaxes the independence assumption by including edge correlations.
• Derived maximum-likelihood estimates for the key parameters of the proposed correlated SBM.
• Proposed a quantitative measure to assess the correlation between different layers in a multilayer network.

Main Results:

• The proposed model demonstrates improved accuracy in inferring community structures and predicting edges compared to traditional SBMs.
• The layer correlation measure effectively captures the similarity in connectivity patterns across network layers.
• Empirical validation on synthetic and real-world temporal network data confirmed the model's effectiveness.

Conclusions:

• Accounting for edge correlations in multilayer networks significantly enhances the performance of community detection and link prediction.
• The developed correlated SBM provides a more realistic framework for analyzing complex systems with interdependent layers.
• This research offers improved tools for understanding and predicting behavior in dynamic and multifaceted network structures.