Let's say I have a graph with $N$ nodes, $A$ arcs and an average branching factor $b$. I want to find the $K$ shortest paths between two nodes.
Is there some relation (even approximate is fine) that expresses the dependency between the parameter $K$ and percentage of nodes included in the paths discovered by running the algorithm (Yen's loopless KSP)?
For example, in a graph of 20 nodes, the ($1st$) shortest path from node $1$ to $12$ is $1-4-7-12$, while the $2nd$ shortest path is $1-4-6-9-12$.
So for $K=1$, the discovered path contains $4/20 = 20\%$ of the nodes in the graph. For $K=2$, the two paths contain $6/20 = 30\%$ of the nodes. This relation between $K$ and the percentage is what I'm looking for.