docs

Author: CarloLucibello

docs/src/messagepassing.md

@@ -18,4 +18,48 @@ where ``\phi`` is expressed by the [`compute_message`](@ref) function,
 ``\gamma_x`` and ``\gamma_e`` by [`update_node`](@ref) and [`update_edge`](@ref)
 respectively.
 
-See [`GraphConv`](ref) and [`GATConv`](ref)'s implementations as usage examples. 
+## An example: implementing the GCNConv
+
+Let's (re-)implement the [`GCNConv`](@ref) layer use the message passing framework.
+The convolution reads 
+```math
+
+```math
+\mathbf{x}'_i = \sum_{j\in N(i)} \frac{1}{c_{ij}} W \mathbf{x}_j
+```
+where ``c_{ij} = \sqrt{N(i)\,N(j)}``. We will also add a bias and an activation function.
+
+```julia
+using Flux
+using GraphNeuralNetworks
+import GraphNeuralNetworks: compute_message, update_node, propagate
+
+struct GCNConv{A<:AbstractMatrix, B, F} <: GNNLayer
+    weight::A
+    bias::B
+    σ::F
+end
+
+Flux.@functor GCNConv
+
+function GCNConv(ch::Pair{Int,Int}, σ=identity; init=glorot_uniform)
+    in, out = ch
+    W = init(out, in)
+    b = zeros(Float32, out)
+    GCNConv(W, b, σ)
+end
+
+compute_message(l::GCNConv, xi, xj, eij) = l.weight * xj
+update_node(l::GCNConv, m, x) = m
+
+function (l::GCNConv)(g::GNNGraph, x::AbstractMatrix{T}) where T
+    g = add_self_loops(g)
+    c = 1 ./ sqrt.(degree(g, T, dir=:in))
+    x = x .* c'
+    x, _ = propagate(l, g, +, x)
+    x = x .* c'
+    return l.σ.(x .+ l.bias)
+end
+```
+
+