Spatial Neighbor Graphs

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

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

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

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