perplexities about triplets() method in DimeNet class

[fedeotto]

I know somebody already asked for clarifications about this function works, but I'm trying to understand what triplets does at a more basic level. I understand that for each directional message m_ji from source index j (row) to target index i (col) we need to consider messages m_kj i.e. all neighbors of the fixed neighbor j of target node i. Let's say that we have a simple graph with 4 nodes and connectivity:

edge_index  :  tensor([[1, 0, 2, 3, 1, 1],
                       [0, 1, 1, 1, 2, 3]])

I understand the assignment row, col = edge_index # j->i (source to target).

Then (I suppose), an adjacency matrix is created by doing:

adj_t = SparseTensor(row=col, col=row, value=value, sparse_sizes=(num_nodes, num_nodes))

why do we transpose row and column here? Also, when we do:

adj_t_row = adj_t[row]

num_triplets = adj_t_row.set_value(None).sum(dim=1).to(torch.long) 

What is the exact meaning of taking adj_t[row] in this context? And why num_triplets is calculated on top of this?

Many thanks in advance and apologize if this was a bit trivial to ask.

[rusty1s]

adj_t refers to the transposed adjacency matrix of (row, col) such that we can index by destination in the first dimension.
Then, adj_t will replicate the adjacencies for every entry in row (it will return a [num_edges, num_nodes] sparse matrix). If we sum this matrix up, then we know the number of triplets (for each edge, we sum up its adjacent nodes).

I agree that the function is very difficult to understand. I suggest to check the output one by one via a simple example.