This problem has been bugging me for weeks now.
Consider a infinite graph, with a given degree distribution. Now, for the sake of intuition, consider that each vertex includes a match. We pick a match and set it on fire. After this, all the adjacent vertices are also ignited.
My question is, what is the average number of match that will be set alight as the propagation from progresses?
A, very, simplistic approach would be that on every iteration the number of newly fired matches is multiplied with the mean degree of the node. However, this ignores the fact that the graph will loop with itself.
What tool could we use to solve this problem? It does smell a bit like generating functions..