GNN when only edge attributes are important [V2]

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

Thanks you very much

[wsad1]

One way to handle this would be to create some node features

1. One feature could be the sum of edge features/weights incident on a node. A similar approach is taken in the ogb-protiens which doesn't have node features.
2. Add node statistics like degree, centrality as features. Read more in 2.1.1 of the graph representation learning book