Problem where only the features of the edges are important.

[MehdiZouitine]

Hello,

I've been stuck with this problem for a few days.
I have a graph where only the weights of the edges are important (TSP with the cost of the edges between each city).
Is there a GNN layer that can learn a good node representation from the edges only?

Another simple problem that I can't solve:
Knowing a graph with weighted edges : train a GNN to predict the total weight of the graph.

I have tried several types of graph convolution but it doesn't work...

Thanks you very much

[Padarn]

Knowing a graph with weighted edges : train a GNN to predict the total weight of the graph.

Can't you just sum the edge weights?

[Padarn]

Is there a GNN layer that can learn a good node representation from the edges only?

Not totally sure what 'good' means here. But maybe this helps, it is the implementation of shorted path problem using GNN (in the graph_nets repo):
https://colab.research.google.com/github/deepmind/graph_nets/blob/master/graph_nets/demos/shortest_path.ipynb

There are a number of papers that (try to) solve this problem, just sharing this one as they have a collab you can explore.

[MehdiZouitine]

That is not the issue. Of course I can do the sum and not use GNN because the problem is trivial.
I would just like to know if a GNN is able to handle a graph with only edge features.

I will take look on the repo !

[Padarn]

I'm not clear on your weight edge sum problem then sorry

[MehdiZouitine]

Do you know how to handle it ?

[Padarn]

Sorry I do not understand what you want to achieve so I can't help. Maybe someone else will be able to help you.

[rusty1s]

I think you should try GraphConv with aggr=sum, and pass edge_weight to its forward call as well.