Clustering determines the dynamics of complex contagions in multiplex networks

Area of Science:

• Network Science
• Mathematical Modeling
• Complex Systems

Background:

• Understanding contagion spread (e.g., influence, information) in interconnected networks is crucial.
• Multiplex networks, with multiple layers of connections, offer a more realistic representation of complex systems.
• Threshold dynamics models explain how individual adoption depends on a fraction of neighbors adopting.

Purpose of the Study:

• To mathematically analyze generalized complex contagions in clustered multiplex networks.
• To investigate the impact of network clustering and link diversity on contagion spread.
• To generalize existing models for content-dependent linear threshold dynamics.

Main Methods:

• Utilized the generating functions formalism for mathematical analysis.
• Developed a generalized linear threshold model accounting for content-dependent link weights.
• Examined conditions, probability, and expected size of global cascades.

Main Results:

• Identified nontrivial dependencies between clustering coefficient and average degree.
• Observed phase transitions in contagion spread based on network descriptors.
• Found that increasing clustering typically decreases cascade probability and size, but this trend reverses at higher average degrees.

Conclusions:

• Network clustering has a complex, degree-dependent effect on contagion spread in multiplex networks.
• Ignoring link types and aggregating network layers can lead to inaccurate contagion dynamics predictions.
• The findings offer a generalized framework for studying spreading phenomena and percolation in complex networks.