Using this definition of path, OP, you must realize that there may be exponentially (in the number of vertices + edges in the graph) many paths between two vertices (even in simple graphs).

Karl Rohe, Tai Qin, Bin Yu, Co-clustering directed graphs to discover asymmetries and directional communities, Proceedings of the National Academy of Sciences of the United States of America, Vol. 113 ...

Some concepts associated with the DACM approach and from the TRIZ method will also be used. Different fields of application of this method based on directed graphs will be presented through different ...