`dgl.``radius_graph`(x, r, p=2, self_loop=False, compute_mode='donot_use_mm_for_euclid_dist', get_distances=False)[source]

Construct a graph from a set of points with neighbors within given distance.

The function transforms the coordinates/features of a point set into a bidirected homogeneous graph. The coordinates of the point set is specified as a matrix whose rows correspond to points and columns correspond to coordinate/feature dimensions.

The nodes of the returned graph correspond to the points, where the neighbors of each point are within given distance.

The function requires the PyTorch backend.

Parameters
• x (Tensor) – The point coordinates. It can be either on CPU or GPU. Device of the point coordinates specifies device of the radius graph and `x[i]` corresponds to the i-th node in the radius graph.

• r (float) – Radius of the neighbors.

• p (float, optional) –

Power parameter for the Minkowski metric. When `p = 1` it is the equivalent of Manhattan distance (L1 norm) and Euclidean distance (L2 norm) for `p = 2`.

(default: 2)

• self_loop (bool, optional) –

Whether the radius graph will contain self-loops.

(default: False)

• compute_mode (str, optional) –

`use_mm_for_euclid_dist_if_necessary` - will use matrix multiplication approach to calculate euclidean distance (p = 2) if P > 25 or R > 25 `use_mm_for_euclid_dist` - will always use matrix multiplication approach to calculate euclidean distance (p = 2) `donot_use_mm_for_euclid_dist` - will never use matrix multiplication approach to calculate euclidean distance (p = 2).

(default: donot_use_mm_for_euclid_dist)

• get_distances (bool, optional) –

Whether to return the distances for the corresponding edges in the radius graph.

(default: False)

Returns

• DGLGraph – The constructed graph. The node IDs are in the same order as `x`.

• torch.Tensor, optional – The distances for the edges in the constructed graph. The distances are in the same order as edge IDs.

Examples

The following examples use PyTorch backend.

```>>> import dgl
>>> import torch
```
```>>> x = torch.tensor([[0.0, 0.0, 1.0],
...                   [1.0, 0.5, 0.5],
...                   [0.5, 0.2, 0.2],
...                   [0.3, 0.2, 0.4]])
>>> r_g = dgl.radius_graph(x, 0.75)  # Each node has neighbors within 0.75 distance
>>> r_g.edges()
(tensor([0, 1, 2, 2, 3, 3]), tensor([3, 2, 1, 3, 0, 2]))
```

When `get_distances` is True, function returns the radius graph and distances for the corresponding edges.

```>>> x = torch.tensor([[0.0, 0.0, 1.0],
...                   [1.0, 0.5, 0.5],
...                   [0.5, 0.2, 0.2],
...                   [0.3, 0.2, 0.4]])
>>> r_g, dist = dgl.radius_graph(x, 0.75, get_distances=True)
>>> r_g.edges()
(tensor([0, 1, 2, 2, 3, 3]), tensor([3, 2, 1, 3, 0, 2]))
>>> dist
tensor([[0.7000],
[0.6557],
[0.6557],
[0.2828],
[0.7000],
[0.2828]])
```