Efficient message passing for cascade size distributions
Abstract
How big is the risk that a few initial failures of networked nodes amplify to large cascades that endanger the functioning of the system? Common answers refer to the average final cascade size. Two analytic approaches allow its computation: (a) (heterogeneous) mean field approximation and (b) belief propagation. The former applies to (infinitely) large locally treelike networks, while the latter is exact on finite trees. Yet, cascade sizes can have broad and multimodal distributions that are not well represented by their average. Full distribution information is essential to identify likely events and to estimate the tail risk, i.e. the probability of extreme events. We therefore present an efficient message passing algorithm that calculates the cascade size distribution in finite networks. It is exact on finite trees and for a large class of cascade processes. An approximate version applies to any network structure and performs well on locally treelike networks, as we show with several examples.
 Publication:

Scientific Reports
 Pub Date:
 April 2019
 DOI:
 10.1038/s41598019428739
 arXiv:
 arXiv:1811.06872
 Bibcode:
 2019NatSR...9.6561B
 Keywords:

 Physics  Physics and Society;
 Nonlinear Sciences  Chaotic Dynamics