Find all paths from source to destination in a weighted cyclic directed graph

Question

I'm trying to find all possible paths from source to destination in a directed graph where edges have weight. There exist cycles but should not lead to infinite loops.

I have used BFS but was unable to detect cycles so that I can consider them as well in the routes.

For example I have the following adjacency list:

'C':['D','E']
'D':['E','C']
'E':['B']
'B':['C']

For source being 'C' and destination being 'C' too, assuming that paths should be no longer than 4 stops, I would have the following routes as result:

CDC CEBC

Answer 1

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