Threshold driven contagion on weighted networks

Area of Science:

• Complex systems science
• Network science
• Dynamical systems

Background:

• Weighted networks represent systems where interaction strength is critical.
• Link weights in networks influence node behavior, essential for processes like social contagion and neural firing.
• Modeling threshold dynamics on weighted networks has been an under-explored area.

Purpose of the Study:

• To investigate threshold dynamics on weighted networks.
• To analyze the impact of weight heterogeneity on cascade emergence.
• To develop a methodology applicable to various binary state processes.

Main Methods:

• Utilized numerical and analytical tools.
• Studied a dynamical threshold model on synthetic and real-world weighted networks.
• Examined the effects of varying weight distributions and network structures.

Main Results:

• Cascade emergence time shows a non-monotonous dependence on weight heterogeneity.
• Weight variations can accelerate or decelerate cascade dynamics.
• Identified non-trivial parameter spaces influenced by network type and weight distributions.

Conclusions:

• Weight heterogeneity plays a significant role in threshold dynamics on complex networks.
• The developed methodology can be applied to diverse binary state processes.
• Understanding edge heterogeneities is crucial for various natural and social phenomena.