Simple Graph Convolution

Definition

Simple graph convolution (SGC) is a simplified variant of GCN. It simplifies GCN without losing much performance by removing the non-linear Activation Function. Due to the simplicity, the SGC can be more computationally efficient, especially for larger graphs. The simplification strategy is very similar to the one used by LightGCN for recommender systems.

The $K$-hops simple graph convolution network for a classification task can be written in ${\hat{Y}}_{\text{SGC}}=\mathrm{softmax}(S^{K}X\Theta )$ where:

• $S=D^{-\frac{1}{2}}(A+I)D^{-\frac{1}{2}}$ is the normalized adjacency matrix for the graph
• $A$ is the Adjacency Matrix of the graph.
• $D$ is the Degree Matrix of the matrix $(A+I)$
• $X$ is the fixed input feature matrix of nodes.
• $\Theta$ is the only weight matrix.

SGC doesn’t require building a computational graph or sample a subgraph, so can be applied for large graphs.