Suppose we have a directed graph $G=(V,E)$ and two nodes $A$ and $B$.I would like to know if there are already algorithms for calculating the following decision problem: Are there at least two paths between $A$ and $B$ of the same length?How about the complexity? Can I solve it in polynomial time?I would like to add a new constrain on the graph, maybe the problem is more solvable.On adjacency matrix, every column is not empty. So, every node has at least one arrow on input and there is also at least one node connected to itself. So if the node is the $i$-th node, then $(i,i)$ is an edge in the graph.
Finding at least two paths of same length in a directed graph
complexity theory;graph theory;time complexity;graphs