Minimum path - all edges at least once

Question

I have a graph with many cycles, possibly tightly coupled, and I need to get a minimal cycle from it. I mean, I need to get a loop, which is the shortest loop in the graph, and each edge is covered at least once.

I was looking for some kind of algorithm or some kind of theoretical background, but the only thing I found was the Chinese postman algorithm. But this solution is not for a directed graph.

Can someone help me? Thanks

Edit → All edges of this graph have the same value - for example, 1

Answer 1

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Answer 2

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Answer 3

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Answer 4

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This algorithm was used by van Aardenden-Ehrenfest and de Bruin to list all Euler tours in a specific oriented graph [1].