Super-Resolution Community Detection for Layer-Aggregated Multilayer Networks.

Area of Science:

• Network Science
• Statistical Physics
• Data Analysis

Background:

• Applied network science often lacks theoretical grounding between data preprocessing and analysis methods.
• Time-varying network data aggregation, a common preprocessing step, has poorly understood trade-offs.
• Detecting small communities in multilayer networks is a challenging problem.

Purpose of the Study:

• To investigate the effects of layer aggregation on detecting small communities in multilayer networks.
• To develop random-matrix theory for analyzing layer-aggregated networks.
• To understand the conditions under which layer aggregation enhances community detection.

Main Methods:

• Developed random-matrix theory for modularity matrices of layer-aggregated Erdős-Rényi networks.
• Studied phase transitions where eigenvectors localize onto planted communities.
• Analyzed the impact of summation-based layer aggregation and thresholding on community detectability limits.

Main Results:

• Summation-based layer aggregation enhances small community detection, especially when the community persists across a varying fraction of layers.
• A phenomenon termed 'super-resolution community detection' was observed, where thresholding causes the detectability limit to decay exponentially.
• Layer aggregation with thresholding acts as a nonlinear filter, enabling detection of otherwise undetectable small communities.

Conclusions:

• Layer aggregation is a powerful preprocessing technique for improving small community detection in multilayer networks.
• Thresholding aggregated network data can significantly enhance community detection sensitivity, achieving super-resolution.
• The choice of threshold is crucial, as different thresholds highlight communities with different properties, and a single threshold may obscure detection.