Neural network approach to phase transitions in clique percolation

Area of Science:

• Complex networks
• Statistical physics
• Machine learning

Background:

• Clique percolation theory studies complete subgraph connectivity, differing from traditional percolation models.
• Conventional simulation methods for clique percolation are computationally intensive and require large system sizes.
• Neural networks present a promising alternative for analyzing complex network phenomena.

Purpose of the Study:

• To investigate the (k,l)-clique percolation phase transition using neural network methods.
• To compare the efficacy of various neural network architectures on Moore lattices and Erdős-Rényi random networks.
• To identify efficient computational approaches for clique percolation analysis.

Main Methods:

• Applied five neural network methods to Moore lattices: matrix-based CNN, FCNN, largest cluster CNN, adjacency matrix CNN, and GCN.
• Utilized two methods for Erdős-Rényi networks: GCN and a fixed lattice CNN.
• Evaluated performance based on the identification of phase transition behaviors.

Main Results:

• Phase transition identification becomes more challenging as k and l increase.
• Matrix-based CNN and largest cluster CNN are effective for Moore lattices.
• GCN excels in ER networks, while fixed lattice CNN identifies specific clique transitions.

Conclusions:

• Neural networks provide effective and computationally efficient tools for studying clique percolation.
• Specific network architectures demonstrate superior performance depending on the network type (Moore lattice vs. ER network).
• This research advances the application of machine learning in complex network analysis.