Spectral analysis and slow spreading dynamics on complex networks

Area of Science:

• Complex Systems
• Network Science
• Statistical Physics

Background:

• The susceptible-infected-susceptible (SIS) model describes spreading phenomena with competing reactions.
• Quenched mean-field (QMF) approximations are used to study disorder effects in scale-free networks.
• QMF accounts for topological heterogeneity and clustering via spectral decomposition.

Purpose of the Study:

• To compare QMF predictions for the SIS model with simulation results on diverse large-dimensional graphs.
• To validate QMF's ability to predict rare-region effects and slow dynamics.
• To investigate Griffiths Phases and their emergence under specific network conditions.

Main Methods:

• Spectral decomposition analysis of adjacency matrices.
• Simulations of the SIS model on Erdős-Rényi, percolating, and generalized Barabási-Albert networks.
• Comparison of QMF predictions with simulation outcomes.

Main Results:

• QMF correctly predicts rare-region effects in Erdős-Rényi graphs.
• QMF provides good estimates for epidemic thresholds in percolating graphs.
• Griffiths Phases are observed in fragmented or weighted networks, and in aging networks, consistent with QMF predictions.

Conclusions:

• QMF is a reliable method for predicting dynamical behavior, rare-region effects, and epidemic thresholds in complex networks.
• The study confirms the emergence of Griffiths Phases in various network configurations.
• Spectral analysis of weighted adjacency matrices accurately predicts simulation dynamics.