Spatial Neighborhood Graph

Edges are formed between nodes (cells or spots) when their Euclidean distance falls below a defined radius threshold. This captures the local microenvironment by connecting entities within a physical interaction range.

• Radius selection is critical: too small creates disconnected components; too large dilutes local signal
• Commonly used in Visium and Slide-seq analysis where spots are arranged on a regular grid
• Enables spatial autocorrelation metrics like Moran's I to quantify expression clustering
• Distance can be measured in pixels, micrometers, or tissue-aware geodesic paths

Each node connects to its k closest neighbors regardless of absolute distance, creating an adaptive graph that accounts for variable cell density across tissue regions.

• Maintains consistent node degree across dense and sparse tissue zones
• Prevents over-connection in cell-dense regions and under-connection in sparse areas
• Standard choice for single-cell spatial data where cell distribution is heterogeneous
• Typical k values range from 5 to 30 depending on tissue complexity

A geometric graph construction that connects nodes to form a triangulation where no point lies inside the circumcircle of any triangle. This produces a planar graph that respects natural tissue boundaries.

• Guarantees spatial coherence without arbitrary threshold selection
• Naturally adapts to irregular cell positions in in situ sequencing data
• Forms the basis for alpha shapes that can identify tissue cavities and boundaries
• Computationally efficient with O(n log n) construction algorithms

Edges carry numerical weights encoding the strength of spatial relationship, often defined as the inverse distance or a Gaussian kernel of distance between nodes.

• Weights decay with distance: w_ij = exp(-d_ij² / 2σ²)
• Enables graph attention mechanisms where closer neighbors exert stronger influence
• Critical for spatial graph neural networks that learn context-aware cell representations
• Weights can incorporate additional modalities like tissue morphology similarity

A message-passing operation where each node aggregates feature information from its spatial neighbors, producing a smoothed representation that captures local tissue context.

• Analogous to convolutional filters in image processing, but operating on irregular graph topology
• Enables detection of spatial domains and tissue compartments through iterative neighborhood aggregation
• Forms the backbone of architectures like GraphSAGE and GAT applied to spatial omics
• Multi-hop convolutions expand the receptive field to capture larger tissue structures

Community detection algorithms partition the spatial graph into coherent tissue domains by optimizing for dense intra-domain connections and sparse inter-domain edges.

• Leiden and Louvain algorithms are standard for identifying spatial niches
• Integrates gene expression similarity with spatial adjacency for biologically meaningful clusters
• Enables spatial domain detection without prior anatomical annotation
• Resolution parameters control the granularity of identified tissue compartments

A statistical measure quantifying the degree to which a gene's expression is dependent on its spatial location. Moran's I ranges from -1 (dispersed) to +1 (highly clustered), with 0 indicating random distribution. A Spatial Neighborhood Graph provides the weight matrix defining which locations are considered neighbors. This analysis is critical for identifying Spatially Variable Genes (SVGs)—genes whose expression patterns are non-random and potentially biologically meaningful, such as those defining tissue boundaries or signaling gradients.

The unsupervised task of partitioning a tissue into anatomically or functionally coherent regions. Algorithms like BayesSpace or SpaGCN use a Spatial Neighborhood Graph to encourage spatial smoothness in cluster assignments. Unlike standard clustering, these methods penalize fragmented assignments, ensuring that identified domains are contiguous. The graph structure allows the model to jointly consider gene expression similarity and physical adjacency, revealing structures like cortical layers in the brain or tumor-immune boundaries.

A computational analysis that identifies spatially proximal cell-type pairs engaged in cell-cell communication. A Spatial Neighborhood Graph is constructed to define which cells are within signaling distance. The analysis then tests for significant co-expression where a ligand gene in a sender cell type and its cognate receptor gene in a neighboring receiver cell type are both highly expressed. Tools like CellChat and NicheNet use this graph-based approach to infer active signaling pathways in the tissue microenvironment.

A computational method for ordering cells based on their spatial coordinates and transcriptomic profiles to reconstruct dynamic processes like differentiation or migration in situ. The Spatial Neighborhood Graph constrains the trajectory to follow physically connected paths, preventing biologically impossible jumps across tissue gaps. Algorithms such as SpaceFlow and stLearn use pseudo-time ordering on the graph to model how cells transition through states while respecting the underlying tissue architecture.

A geometric method for building a Spatial Neighborhood Graph from cell centroid coordinates. Unlike fixed-radius or k-nearest neighbor approaches, Delaunay triangulation connects points such that no point lies inside the circumcircle of any triangle. This creates a planar graph that naturally respects tissue topology, avoiding long-range edges across empty spaces. It is particularly useful for single-cell resolution data where cell density varies, providing an adaptive neighborhood definition without arbitrary distance thresholds.