Where the following propagation model arise in practice
Imagine each node in your graph as a user, and each edge as an action such as 'share'. It may also be a bidirectional relationship 'share' and 'view'.

Some social scientists and engineers estimate the probability that a message is 'shared' and 'viewed' given that a particular user decides to share it. This process is called "information diffusion", "information propagation", "cascading", etc.

If you are interested in the details of how these calculations are performed, check out these papers:

http://cs.stanford.edu/people/jure/pubs/netrate-netsci14.pdf

http://cs.stanford.edu/people/jure/pubs/cascades-www14.pdf

http://cs.stanford.edu/people/jure/pubs/infopath-wsdm13.pdf

Similar topics:
http://snap.stanford.edu/papers.html