Regression with Graph Convolutional Networks

I am writing my MSc. thesis at the moment. I want to optimise a strategy on how to efficiently distribute a constrained budget B among some network nodes.

Let’s say my network consists of 120 nodes and it is a directed network. Each edge has one feature/weight. My budget constraint is B <= number of nodes = 120.

Input for my Graph Convolutional Network is the specific fixed network topology as graph G and a budget distribution x that are my node features as well as my edge_index and my edge_weights.

My target is 1 scalar for a distribution x among 120 nodes, not a classification problem.

Is there a specific architecture that is relevant for this task. For instance, I added 1 linear layer after convolution, then global pooled to get a graph-level output, but the simple 2 layer GCN + 1 Linear Layer network works poorly and does not learn.

Any suggestions are highly appreciated…