When the structure and edges are all the same

I am dealing with many large graphs where the structure and edge values are the same. The node values, however, vary greatly.

# structure and edge values are the same in every graph
# but node values vary in each graph
graph 1 = (node: 2.1)-[edge: 1.0]-(node: 3.6)-[edge: 4.5]-(node: 5.7)
graph 2 = (node: 1.8)-[edge: 1.0]-(node: 2.9)-[edge: 4.5]-(node: 6.2)

Since the structure of the graphs does not vary, does it even make sense to use a GNN? The number of edges is exponential to the number of nodes, so would a GNN be wasting a lot of time constructing edge-based embeddings/ matrixes, or do I still need to know at least which nodes are connected to which other nodes?

Alternatively, I was thinking about training a regular 1D CNN or LSTM on the features of each node, but I am worried that they will misinterpret the nodes to be ordered sequentially.

Is there an obvious kind of GNN model for this use case?

I think whether GNNs help here depends on whether the graph topology is meaningful. If so, GNNs may still help.

By “the number of edges is exponential to the number of nodes”, do you suggest that the graphs are very dense?

GNNs do not necessarily need to learn edge-based embeddings from scratch. Actually most GNNs use node features only.

@mufeili yes, literally dense, but not complete graphs.

I will run both a 1D CNN (filter_size=1) and GCN (without edge values) to see how their learning rates compare.