Generative models for two-ground-truth partitions in networks.

Area of Science:

• Network science
• Graph theory
• Statistical modeling

Background:

• Characterizing mesoscale network structure often involves partitioning nodes into communities, blocks, or clusters.
• Existing methods may yield diverse and conflicting results, even with repeated runs, indicating potential ambiguity in detected partitions.

Purpose of the Study:

• To introduce the stochastic cross-block model (SCBM) for generating benchmark networks with coexisting, distinct mesoscale partitions.
• To evaluate the capability of stochastic block models (SBMs) to detect these coexisting structures.

Main Methods:

• Development of the stochastic cross-block model (SCBM) to embed two distinct partitions within a single network.
• Experimental assessment of various stochastic block model (SBM) variants using SCBM-generated benchmark networks.

Main Results:

• The ability of SBMs to detect individual partitions varied by SBM variant.
• Coexisting bicommunity and core-periphery structures were rarely recovered simultaneously.
• Often, only a single, dominant structure was detected, even when multiple partitions were present.

Conclusions:

• Existing SBMs have limited power to detect coexisting mesoscale structures in networks.
• Highlighting the need to consider partition landscapes and develop methods for detecting partition coexistence.
• The SCBM provides a valuable tool for benchmarking network analysis methods and exploring structural ambiguity.