If I'm not misunderstanding, you may use NetworkX to do that.

For a simple example.

First, create an undirected graph.

G = nx.Graph()

Then you can add some edges,

G.add_edge('A', 'B')

G.add_edge('B', 'C')

G.add_edge('C', 'D')

G.add_edge('D', 'E')

G.add_edge('E', 'F')

Then we can define a function to get two edges v1 and v2.

def detour_distance(graph, v1, v2):

we can use nx.all_pairs_shortest_path_length() to find all path among all edges.

all_simple_paths = list(nx.all_simple_paths(graph, v1, v2))

Then calculate the length of every path(edge num, use 1 as default)

all_path_lengths = [len(path) - 1 for path in all_simple_paths]

Return the maximum path length

return max(all_path_lengths)

print(detour_distance(G, 'A', 'E')) # 4

print(detour_distance(G, 'A', 'B')) # 1

you may ask Yiren Wang he's professional.

Correct me if any wrong.