<!--

COPYRIGHT NOTICE

This file is part of the "Universal Biomedical Skills" project.

Copyright (c) 2026 MD BABU MIA, PhD <md.babu.mia@mssm.edu>

All Rights Reserved.

#

This code is proprietary and confidential.

Unauthorized copying of this file, via any medium is strictly prohibited.

#

Provenance: Authenticated by MD BABU MIA

-->

Spatial Neighbor Graphs

Build spatial neighbor graphs for connectivity-based analyses.

Required Imports

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

Build K-Nearest Neighbors Graph

python
# 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

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

Radius-Based Neighbors

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

For Visium Data (Grid Structure)

python
# 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

python
# 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

python
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

python
# 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

python
# 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

python
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

python
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

python
# 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

<!-- AUTHOR_SIGNATURE: 9a7f3c2e-MD-BABU-MIA-2026-MSSM-SECURE -->