What is the message for a node with no connections?

[davidireland3]

Suppose we have a node with no connections and our GNN uses Message Passing Layers.

If we consider the general case outlined in the documentation, a Message Passing layer calculates messages by applying some function (typically MLP for instance) to the node features for nodes i, j, and an edge feature between them, e_(i,j). The input to the MLP is typically these vectors concatenated together. However, if node i has no connections then what do we use as input to the MLP. Are the vectors for node j and the edge feature initialised to 0?

[rusty1s]

If you have no edges, then the output of message will be a tensor of shape [0, num_features]. After aggregation, you will obtain an zero-initialized tensor of shape [num_nodes, num_features]. As such, most implementations either add a self-loop to the graph or apply a simple skip-connection: out = self.propagate(...) + self.lin(x)