first of all I want to mention, that I'm pretty new to graph-theory. Currently I'm about to write a path search algorithm and I want to take advantage of previous knowledge.
So this is the setup: -the graph is fully connected
-the graph is directed
-number of states are given
-number of edges are given
-the graph displays a markovchain, so all outgoing edges of a node have to be 1, summed up
-there is one input node and one output node, no more absorbing states
before the algorithm starts i want to estimate the probability of the most probable path.
I was thinking about: what is the most probable graph structure, what would be the average connectivity and how would the probability distribution be.
like I said before I'm new to this, so this might be stupid or to easy or impossible :P