Explosive Percolation in the Human Protein Homology Network

TL;DR

This paper investigates the explosive percolation transition in the Human Protein Homology Network, revealing a sudden emergence of a giant cluster similar to first-order phase transitions, driven by slow-growing isolated modules.

Contribution

It demonstrates that the H-PHN exhibits explosive percolation behavior akin to Achlioptas processes, linking network topology evolution to first-order transition characteristics.

Findings

H-PHN shows explosive percolation similar to Achlioptas processes.

The transition involves slow-growing clusters that rapidly connect later.

Results suggest evolutionary processes can cause sudden topological changes.

Abstract

We study the explosive character of the percolation transition in a real-world network. We show that the emergence of a spanning cluster in the Human Protein Homology Network (H-PHN) exhibits similar features to an Achlioptas-type process and is markedly different from regular random percolation. The underlying mechanism of this transition can be described by slow-growing clusters that remain isolated until the later stages of the process, when the addition of a small number of links leads to the rapid interconnection of these modules into a giant cluster. Our results indicate that the evolutionary-based process that shapes the topology of the H-PHN through duplication-divergence events may occur in sudden steps, similarly to what is seen in first-order phase transitions.