Hi, I’m using the `gomory_hu_tree`

function, but I’ve run into an issue. I’m wondering if the function is actually returning an equivalent flow tree and *not* the Gomory Hu tree (as discussed in Gusfield 1990)? Although I might have misunderstood something.

I’ve created a MWE (in python igraph), using G a K4 graph. It gives a Gomory Hu tree that is a path (0–1–2–3), with all edges weight 3.

In a Gomory Hu Tree, for given vertices x,y, the smallest weight edge e on the x-y path in T induces a cut represented by the components of T-e that is a minimum x-y cut in G.

However if we take x,y to be 1,2 in the MWE, the cut induced by the only edge e on the 1-2 path induces a cut ({0,1}, {2,3}) in G, which is weight 4, and *not* a minimum 1-2 cut in G.

So it seems like the tree returned by the function is a correct equivalent flow tree, but not a Gomory Hu tree.

The Gomory Hu tree of K4 should be a star, with all edges weight 3.

MWE

```
import igraph as ig
G= ig.Graph.Full(n=4)
T = G.gomory_hu_tree(flow="label")
visual_style = {}
visual_style["vertex_color"] = "white"
visual_style["vertex_label"] = range(4)
ig.plot(T, **visual_style)
```

My apologies in advance if I’ve misunderstood something.

Thanks

Michal