Common longest and shortest path in graphs
If you have graphs with the same set of nodes (V1,...,VN) (if some nodes are unique that it does not matter, you simply ignore them as they cannot be the part of any common path) and want to find a shortest/longest path you can proceed as follows:

Generate the intersection of all the graphs, that is: a graph, that has  nodes (V1,...,VN) and node Vi is connected to Vj iff in all your graphs Vi is connected to Vj. If you have adjacency matrices of each graph, it is just an element-wise multiplication of this matrices
Find the shortest/longest path in the resulting graph, it has a guarantee to be the shortest (between some two vertices I suppose?) /longest (common) among all of them.
I need a hint were to look algo ( maybe even in python )
So I have huge amount of graphs some, and I need to find common shortest and longest path for this graphs. or common parts ( shortest or longest )
Upd for more clear describing:
Before analysis graphs already have connections between nodes ? so they are already like a path.
And as result it's needed to have common possible path for all graphs depending on connections between nodes