Algorithm 1 Framework of the GEA

Input: Graph with node set V, node embeddings X

Output: Updated node representations $X_{\mathrm{out}}$

1: Initialize model parameters: external key-value units $U_k$, $U_v$, and number of heads $H_{ext}$

2: for each node $\in X$ do

3:    $X_{\mathrm{reshaped}}=\mathrm{Reshape}(X,(n,\begin{array}{c}\hfill H_{ext}\end{array},d/\begin{array}{c}\hfill H_{ext}\end{array}))$

4:    $Q=X_{\mathrm{reshaped}}{U}_k^T$

5:    $A=\mathrm{DNorm}\left(Q\right)$

6:    $X_{\mathrm{attn}}=A{U}_v$

7:    $X_{\mathrm{out}}=\mathrm{Reshape}(X_{\mathrm{attn}},(n,d))$

8: end for

9: return $X_{\mathrm{out}}$