GCN can be viewed as a more complex form of message passing with additional trainable weights and non-linearities. Suppose we combine a simple graph convolution via polynomial $\mathbf{A}+\mathbf{I}$, then we can have:

$\mathbf{H}^{(k)}=\sigma(\mathbf{A} \mathbf{H}^{(k-1)} \mathbf{W}_{neigh}^{(k)} + \mathbf{H}^{(k-1)} \mathbf{W}_{self}^{k})$

We can see that a graph convolution based on $\mathbf{I}+\mathbf{A}$ is equivalent to first aggregate neighborhood information and then combining it with information of the node-self.