Interevent time distribution, burst, and hybrid percolation transition

Area of Science:

• Complex networks
• Statistical physics
• Network science

Background:

• Hybrid percolation transitions (HPTs) are characterized by a jump in giant cluster size and critical behavior in finite clusters.
• Understanding the mechanisms driving HPTs, particularly those involving cluster coalescence, is crucial for network science.
• Existing models often focus on pruning processes, leaving the dynamics of cluster merging less explored.

Purpose of the Study:

• To elucidate the underlying mechanism of hybrid percolation transitions (HPTs) induced by cluster coalescence.
• To investigate the self-organized critical (SOC) behavior associated with cluster set crossings during HPTs.
• To identify predictive signals for abrupt transitions in network structures.

Main Methods:

• Utilized a restricted-random network model where clusters are ranked by size and divided into small- and large-cluster sets.
• Analyzed cluster movements across set boundaries as rankings are updated during cluster merging.
• Characterized the cluster size distribution and identified power-law exponents for crossing intervals.

Main Results:

• Discovered that intervals of cluster set crossings exhibit self-organized critical (SOC) behavior with two power-law exponents.
• Observed the formation and elimination of a bump in the cluster size distribution, signifying HPT criticality.
• Found that a burst of crossing events precedes and signals an upcoming abrupt transition.

Conclusions:

• The study reveals an SOC mechanism governing HPTs via cluster coalescence, distinct from pruning-driven avalanche dynamics.
• The identified SOC behavior and crossing events provide a new framework for understanding and predicting network transitions.
• A burst of cluster set crossing events serves as a critical precursor to abrupt changes in network structure.