Version Compatibility

Reference examples tested with: matplotlib 3.8+, numpy 1.26+, scanpy 1.10+, scikit-learn 1.4+, scipy 1.12+, squidpy 1.3+

Before using code patterns, verify installed versions match. If versions differ:

• Python:

  pip show <package>

  then

  help(module.function)

  to check signatures

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Spatial Neighbor Graphs

"Build a spatial neighborhood graph" → Construct spatial connectivity graphs using k-nearest neighbors, Delaunay triangulation, or radius-based methods for downstream spatial statistics.

• Python:

  squidpy.gr.spatial_neighbors(adata, coord_type='generic', n_neighs=6)

Build spatial neighbor graphs for connectivity-based analyses.

Required Imports

import squidpy as sq
import scanpy as sc
import numpy as np

Build K-Nearest Neighbors Graph

Goal: Construct a spatial KNN graph connecting each spot to its nearest spatial neighbors.

Approach: Use Squidpy's

spatial_neighbors

with k-nearest neighbors on coordinate distances.

# Build spatial KNN graph
sq.gr.spatial_neighbors(adata, n_neighs=6, coord_type='generic')

# Check the graph
print(f"Connectivities shape: {adata.obsp['spatial_connectivities'].shape}")
print(f"Distances shape: {adata.obsp['spatial_distances'].shape}")

Build Delaunay Triangulation Graph

# Delaunay triangulation (natural neighbors)
sq.gr.spatial_neighbors(adata, delaunay=True, coord_type='generic')

Radius-Based Neighbors

# Connect all spots within a radius
sq.gr.spatial_neighbors(adata, radius=100, coord_type='generic')

For Visium Data (Grid Structure)

# For Visium hexagonal grid, use n_rings
sq.gr.spatial_neighbors(adata, n_rings=1, coord_type='grid')  # 6 immediate neighbors
sq.gr.spatial_neighbors(adata, n_rings=2, coord_type='grid')  # Extended neighborhood

Access Neighbor Information

# Get connectivities as sparse matrix
conn = adata.obsp['spatial_connectivities']
print(f'Edges in graph: {conn.nnz}')
print(f'Mean neighbors per spot: {conn.nnz / adata.n_obs:.1f}')

# Get distances
dist = adata.obsp['spatial_distances']
nonzero_dist = dist.data[dist.data > 0]
print(f'Mean neighbor distance: {nonzero_dist.mean():.1f}')

Get Neighbors for a Specific Spot

from scipy.sparse import csr_matrix

spot_idx = 0
conn = adata.obsp['spatial_connectivities']

# Get neighbor indices
neighbor_indices = conn[spot_idx].nonzero()[1]
print(f'Spot {spot_idx} has {len(neighbor_indices)} neighbors: {neighbor_indices}')

# Get distances to neighbors
dist = adata.obsp['spatial_distances']
neighbor_distances = dist[spot_idx, neighbor_indices].toarray().flatten()
print(f'Distances: {neighbor_distances}')

Build Expression-Based Neighbors

# Standard expression-based neighbors (for comparison)
sc.pp.neighbors(adata, n_neighbors=15, n_pcs=30)

# Now adata has both:
# - adata.obsp['spatial_connectivities'] (spatial)
# - adata.obsp['connectivities'] (expression)

Combine Spatial and Expression Neighbors

Goal: Create a unified neighbor graph that balances spatial proximity with expression similarity.

Approach: Build separate spatial and expression neighbor graphs, normalize each, then combine with a tunable weight parameter.

# Build both graphs
sq.gr.spatial_neighbors(adata, n_neighs=6, coord_type='generic')
sc.pp.neighbors(adata, n_neighbors=15, n_pcs=30)

# Weighted combination (manual)
alpha = 0.5  # Weight for spatial vs expression
spatial_conn = adata.obsp['spatial_connectivities']
expr_conn = adata.obsp['connectivities']

# Normalize and combine
from sklearn.preprocessing import normalize
spatial_norm = normalize(spatial_conn, norm='l1', axis=1)
expr_norm = normalize(expr_conn, norm='l1', axis=1)
combined = alpha * spatial_norm + (1 - alpha) * expr_norm

adata.obsp['combined_connectivities'] = combined

Visualize Neighbor Graph

Goal: Display the spatial neighbor graph overlaid on tissue coordinates for visual inspection.

Approach: Draw edges between connected spots and scatter plot the spot positions.

import matplotlib.pyplot as plt

# Get coordinates
coords = adata.obsm['spatial']
conn = adata.obsp['spatial_connectivities']

fig, ax = plt.subplots(figsize=(10, 10))

# Draw edges
rows, cols = conn.nonzero()
for i, j in zip(rows, cols):
    if i < j:  # Avoid drawing twice
        ax.plot([coords[i, 0], coords[j, 0]], [coords[i, 1], coords[j, 1]], 'k-', alpha=0.1, linewidth=0.5)

# Draw nodes
ax.scatter(coords[:, 0], coords[:, 1], s=10, c='blue', alpha=0.5)
ax.set_aspect('equal')
plt.title('Spatial neighbor graph')

Compute Graph Statistics

Goal: Calculate summary statistics of the spatial neighbor graph (nodes, edges, connectivity).

Approach: Convert the sparse connectivity matrix to a NetworkX graph and compute standard graph metrics.

import networkx as nx
from scipy.sparse import csr_matrix

conn = adata.obsp['spatial_connectivities']
G = nx.from_scipy_sparse_array(conn)

print(f'Nodes: {G.number_of_nodes()}')
print(f'Edges: {G.number_of_edges()}')
print(f'Average degree: {2 * G.number_of_edges() / G.number_of_nodes():.2f}')
print(f'Connected components: {nx.number_connected_components(G)}')

Store Multiple Neighbor Graphs

# Store different neighborhood sizes
for n_neighs in [4, 6, 10]:
    sq.gr.spatial_neighbors(adata, n_neighs=n_neighs, coord_type='generic')
    adata.obsp[f'spatial_conn_{n_neighs}'] = adata.obsp['spatial_connectivities'].copy()
    adata.obsp[f'spatial_dist_{n_neighs}'] = adata.obsp['spatial_distances'].copy()

Related Skills

• spatial-statistics - Use neighbor graph for spatial statistics
• spatial-domains - Identify domains using spatial graph
• single-cell/clustering - Non-spatial neighbor graphs