Cascades on Networks with Functional Structure
Provides theoretical insights into how network functional organization affects cascading failures, relevant for understanding systemic risk in interdependent systems.
The paper analyzes cascade dynamics on directed multiplex networks with functional structure, deriving exact expressions for cascade size and probability, and showing that functional structure significantly alters phase transitions.
We consider a version of the Watts threshold model on directed multiplex configuration model networks, and present a detailed analysis of the cascade size, single-seed cascade probability and cascade condition. We then introduce a smaller class of network models that we call "constrained multiplex networks", which is designed to represent networks with so-called "functional" or "complementary" structure. We find that the particular choice of functional structure affects the phase transitions of the cascade model in a variety of ways.