Spatial Neighbor Graphs
Build spatial neighbor graphs for connectivity-based analyses.
Required Imports
import squidpy as sq
import scanpy as sc
import numpy as npBuild K-Nearest Neighbors Graph
# 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 neighborhoodAccess 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
# 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'] = combinedVisualize Neighbor Graph
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
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