Define graph entities

[hkim716]

Hi Matt,
I re-open this discussion to discuss my problem setting with you.
I'd like to predict delay time between several cities using GNN. I will make temporal graphs depending on time steps e.g. a graph with time step t=0, 1, 2, ...
Several cities can be linked each other with edges so we can have large directional graphs for each time step.

In this case, one transportation can be thought of 1 directional edge, and each node will have the location (x, y) or weather informations at each time step. Each edge will have travel information as edge features like departure time , arrival time, distance, average speed, and so on.
However, there might be several ways to transport between the same city A -> B, such as by train, airplane, walk, bicycle, car, and so on. In that case, edge_index should be the same, but how can we have different edge types depending on method of transportation?
I think the goal is to predict labels which is delay time for each edge.

My graph entities will look like this :
node : cities
edge_index : (num_edge, 2)
pos (if needed): location of node in (x , y) coordinates
node_feature : (x, y), or weather information
edge_attribute: departure time , arrival time, distance, speed between the two cities
label : delay_time (I think it's property of edges, so is it link prediction regression problem?)

Since city locations are determined by (x, y) location, nodes do not have types .
How can I apply different edge types in PyG? I mean, how can I differentiate edges even for the same route A -> B? Is it differentiated by edge_attribute so it can have more edge attributes in there? I'm thinking like this:

e.g. 1st edge edge_attr: distance, method of transport type in one-hot encoding = (239 , [1, 0, 0, 0, 0])
2nd edge edge_attr: distance, method of transport type in one-hot encoding = (47 , [0, 1, 0, 0, 0])
...
nth edge edge_attr: distance, method of transport type in one-hot encoding = (683 , [0, 0, 0, 1, 0])

Long story short :
Does this look correct graph entities for using GNN in PyG?
In that direction, at each time step, nodes are static, but edges will be always changing, and there can be multiple edges between the same nodes with different edge attribute. (I don't want to make my graphs too complicated. I want to make graphs as static as possible..)
If there’s no travel between two nodes, they will be isolated node, is it ok for a GNN to take isolated graph as their inputs?

Sorry for many questions, but thanks in advance!

[wsad1]

Does this look correct graph entities for using GNN in PyG?

Yeah this seems like the right representation. It does look like a link regression problem. You could add an edge_type argument and use and RGCN like done in this example to model your problem. Although that example is link prediction you could modify the loss and remove negative sampling to make it link regression.

If there’s no travel between two nodes, they will be isolated node, is it ok for a GNN to take isolated graph as their inputs?

Yeah that shouldn't be a problem mostly.