import torch
from torch_geometric.data import Data
from torch_geometric.data.datapipes import functional_transform
from torch_geometric.transforms import BaseTransform
from torch_geometric.utils import coalesce, remove_self_loops, scatter
[docs]@functional_transform('line_graph')
class LineGraph(BaseTransform):
r"""Converts a graph to its corresponding line-graph
(functional name: :obj:`line_graph`):
.. math::
L(\mathcal{G}) &= (\mathcal{V}^{\prime}, \mathcal{E}^{\prime})
\mathcal{V}^{\prime} &= \mathcal{E}
\mathcal{E}^{\prime} &= \{ (e_1, e_2) : e_1 \cap e_2 \neq \emptyset \}
Line-graph node indices are equal to indices in the original graph's
coalesced :obj:`edge_index`.
For undirected graphs, the maximum line-graph node index is
:obj:`(data.edge_index.size(1) // 2) - 1`.
New node features are given by old edge attributes.
For undirected graphs, edge attributes for reciprocal edges
:obj:`(row, col)` and :obj:`(col, row)` get summed together.
Args:
force_directed (bool, optional): If set to :obj:`True`, the graph will
be always treated as a directed graph. (default: :obj:`False`)
"""
def __init__(self, force_directed: bool = False):
self.force_directed = force_directed
def forward(self, data: Data) -> Data:
N = data.num_nodes
edge_index, edge_attr = data.edge_index, data.edge_attr
edge_index, edge_attr = coalesce(edge_index, edge_attr, num_nodes=N)
row, col = edge_index
if self.force_directed or data.is_directed():
i = torch.arange(row.size(0), dtype=torch.long, device=row.device)
count = scatter(torch.ones_like(row), row, dim=0,
dim_size=data.num_nodes, reduce='sum')
cumsum = torch.cat([count.new_zeros(1), count.cumsum(0)], dim=0)
cols = [
i[cumsum[col[j]]:cumsum[col[j] + 1]]
for j in range(col.size(0))
]
rows = [row.new_full((c.numel(), ), j) for j, c in enumerate(cols)]
row, col = torch.cat(rows, dim=0), torch.cat(cols, dim=0)
data.edge_index = torch.stack([row, col], dim=0)
data.x = data.edge_attr
data.num_nodes = edge_index.size(1)
else:
# Compute node indices.
mask = row < col
row, col = row[mask], col[mask]
i = torch.arange(row.size(0), dtype=torch.long, device=row.device)
(row, col), i = coalesce(
torch.stack([
torch.cat([row, col], dim=0),
torch.cat([col, row], dim=0)
], dim=0),
torch.cat([i, i], dim=0),
N,
)
# Compute new edge indices according to `i`.
count = scatter(torch.ones_like(row), row, dim=0,
dim_size=data.num_nodes, reduce='sum')
joints = torch.split(i, count.tolist())
def generate_grid(x):
row = x.view(-1, 1).repeat(1, x.numel()).view(-1)
col = x.repeat(x.numel())
return torch.stack([row, col], dim=0)
joints = [generate_grid(joint) for joint in joints]
joints = torch.cat(joints, dim=1)
joints, _ = remove_self_loops(joints)
N = row.size(0) // 2
joints = coalesce(joints, num_nodes=N)
if edge_attr is not None:
data.x = scatter(edge_attr, i, dim=0, dim_size=N, reduce='sum')
data.edge_index = joints
data.num_nodes = edge_index.size(1) // 2
data.edge_attr = None
return data