Enhanced Detectability of Community Structure in Multilayer Networks through Layer Aggregation.

Area of Science:

• Network Science
• Statistical Physics
• Data Analysis

Background:

• Multilayer networks represent complex systems with multiple interaction types.
• Detecting community structure is crucial for understanding network organization.
• Limitations in detecting communities in multilayer networks are not fully understood.

Purpose of the Study:

• Analyze detectability limitations for community structure in multilayer networks.
• Investigate the impact of layer aggregation methods on community detection.
• Provide insights into thresholding practices for sparse network representations.

Main Methods:

• Utilized random matrix theory to analyze multilayer stochastic block models (SBMs).
• Studied multiplex SBMs where layers originate from a common SBM.
• Examined various layer aggregation techniques, including matrix summation and thresholding.

Main Results:

• The detectability limit for community structure vanishes as O(L^{-1/2}) with an increasing number of layers (L) when using matrix summation.
• Similar vanishing behavior was observed when layer summation is optimally thresholded.
• Demonstrated that layer aggregation can obscure community structure in multilayer networks.

Conclusions:

• Layer aggregation methods significantly impact the detectability of community structure in multilayer networks.
• The practice of thresholding interaction data can be understood through the lens of aggregation effects.
• Understanding these limitations is key for accurate analysis of complex systems represented by multilayer networks.