cards/graph/graph-convolution-operator/

[giscus[bot]]

cards/graph/graph-convolution-operator/

For a given graph $\mathcal G$, we have an attribute on each node, denoted as $f_v$. All the node attributes put together can be written as a list $\mathbf f\to (f_{v_1}, f_{v_2}, \cdots, f_{v_N})$.
Convolution on graph is combining attributes on nodes with their neighbors'. The adjacency matrix Graph Adjacency Matrix A graph $\mathcal G$ can be represented with an adjacency matrix $\mathbf A$. There are some nice and clear examples on wikipedia1, for example, $$ \begin{pmatrix} 2 & 1 & 0 & 0 & 1 & 0\ 1 & 0 & 1 & 0 & 1 & 0\ 0 & 1 & 0 & 1 & 0 & 0\ 0 & 0 & 1 & 0 & 1 & 1\ 1 & 1 & 0 & 1 & 0 & 0\ 0 & 0 & 0 & 1 & 0 & 0 \end{pmatrix} $$ for the graph Public Domain, Link $\mathbf A$ applied on all node attributes $\mathbf f$ is such an operation, i.

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