Local Phase Transitions in a Model of Multiplex Networks with Heterogeneous Degrees and Inter-Layer Coupling

Area of Science:

• Complex Systems Science
• Network Science
• Statistical Physics

Background:

• Multilayer networks describe systems with multiple types of connections among the same nodes.
• Distinguishing true inter-layer dependencies from spurious correlations due to node heterogeneity is crucial for understanding multiplexes.

Purpose of the Study:

• To develop an unbiased model for multiplexes that can control intra-layer node degrees and inter-layer overlap.
• To provide a method for disentangling spurious correlations from true inter-layer dependencies in multilayer networks.

Main Methods:

• Introduction of an unbiased maximum entropy model for multiplexes.
• Mapping the model to a generalized Ising model to study phase transitions.
• Quantifying the contributions of node heterogeneity and inter-layer coupling to overlap.

Main Results:

• Node heterogeneity can lead to link-specific phase transitions, increasing overlap.
• The model successfully quantifies how spurious and true correlations contribute to overlap.
• Analysis of the International Trade Multiplex reveals a genuine need for inter-layer coupling.

Conclusions:

• The developed model effectively disentangles spurious correlations from true inter-layer dependencies in multilayer networks.
• Empirical evidence from the International Trade Multiplex supports the necessity of modeling inter-layer coupling.