Communities, clustering phase transitions, and hysteresis: pitfalls in constructing network ensembles

Area of Science:

• Network science
• Statistical physics

Background:

• Ensemble networks are common null models.
• Simple null models often lack real-world network clustering.

Purpose of the Study:

• Investigate a biased rewiring model to enhance network clustering.
• Preserve node degrees while incorporating triangle formation (fugacity).

Main Methods:

• Studied a biased rewiring model with fugacity.
• Analyzed phase transitions in regular and nonregular networks.
• Introduced q-clique adjacency plots for visualization.

Main Results:

• Phase transitions observed with changes in fugacity.
• Emergence of "cluster cores" in nonregular networks.
• Cluster cores are robust communities with high interconnectedness and hysteresis.

Conclusions:

• Clustering is not uniformly distributed but concentrated in cluster cores.
• Cluster cores act as emergent, robust communities.
• Hysteresis in cluster core formation poses challenges for null model applications.