K shortest paths - any relation between K and % of graph nodes in discovered paths? 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.
It seems to me the relation depends purely on how the graph is made. Think about a cycle. The shortest path between two adjacent vertices contains 2 vertices while the second contains n vertices