Normalize an Adjacency Matrix

Prepare a sparse adjacency matrix for message passing.

• gcn_normalize() applies the symmetric normalization \(D^{-1/2} A D^{-1/2}\) of Kipf and Welling (2017).

• adj_row_normalize() applies the row normalization \(D^{-1} A\), so that the weights of each node's neighbors sum to one.

• add_graph_self_loops() replaces any existing diagonal entries with unit self-loops, giving \(A + I\).

Isolated nodes have degree zero. Their normalization factor is set to zero rather than being allowed to diverge, so they contribute nothing to the aggregation.

Usage

gcn_normalize(adj)

adj_row_normalize(adj)

add_graph_self_loops(adj)

Arguments

adj

Sparse COO torch_tensor n_nodes x n_nodes. The adjacency matrix, which may be weighted.

Value

A coalesced sparse COO torch_tensor of the same dimension as adj.

References

Kipf, T. N., & Welling, M. (2017). Semi-supervised classification with graph convolutional networks. International Conference on Learning Representations. doi:10.48550/arXiv.1609.02907

Examples

if (FALSE) { # torch::torch_is_installed()
adj <- adj_from_edgelist(from = c(1, 2, 3), to = c(2, 3, 1))

gcn_normalize(adj)

adj_row_normalize(adj)

# The usual pre-processing for a GCN layer
gcn_normalize(add_graph_self_loops(adj))
}