GCN docs

[meyerTUM]

In the docs of GCN it says:

Its node-wise formulation is given by:
.. math::
    \mathbf{x}^{\prime}_i = \mathbf{\Theta} \sum_{j}
    \frac{1}{\sqrt{\hat{d}_j \hat{d}_i}} \mathbf{x}_j
with :math:`\hat{d}_i = 1 + \sum_{j \in \mathcal{N}(i)} e_{j,i}`, where
:math:`e_{j,i}` denotes the edge weight from source node :obj:`i` to target
node :obj:`j` (default: :obj:`1`)

Shouldn't it be instead:

\mathbf{x}^{\prime}_i = \mathbf{\Theta} \sum_{j}
\frac{e_{j,i}}{\sqrt{\hat{d}_j \hat{d}_i}} \mathbf{x}_j

Only if there is an edge between node i and node j, node j should contribute, right?

[rusty1s]

You are right. That is a typo. Ofc, the j only iterates over the neighbors of i. This is now fixed in master.

[meyerTUM]

Maybe I am missing something, but shouldn't x_j be weighted with the edge weight e_{j,i} and the formula only describes the default case, where all edge weights are set to 1.0?

So, shouldn't e_{j,i} be in the numerator of the fraction? Am I missing something? Thanks for taking your time! I appreciate it.

[rusty1s]

Oh yeah, you are absolutely right. I really missed that. This should now be finally fixed :) Thanks once again!