Graph-Based Clustering

The foundational step where each cell is connected to its k most similar neighbors based on a distance metric (typically Euclidean distance in PCA space). This transforms the data into a graph object where nodes represent cells and edges represent transcriptomic similarity. The choice of k directly influences cluster resolution—smaller values detect fine substructure, while larger values produce broader groupings.

Raw k-NN graphs are refined into a Shared Nearest Neighbor graph to emphasize robust connections. The edge weight between two cells is calculated based on the overlap in their neighborhoods (Jaccard index). This step effectively denoises the graph by down-weighting spurious connections and strengthening edges between cells that share many common neighbors, improving cluster separation.

A greedy optimization algorithm that partitions the graph by iteratively moving nodes between communities to maximize modularity—a measure comparing edge density within communities versus a random null model. Louvain is computationally fast and widely implemented in tools like Seurat and Scanpy, though it can occasionally produce arbitrarily badly connected communities.

An improvement over Louvain that guarantees well-connected communities by adding an intermediate refinement phase after the initial partition. The Leiden algorithm runs through three phases: local moving, refinement, and network aggregation. This ensures that all clusters are internally connected subgraphs, avoiding the fragmentation artifacts sometimes observed with Louvain. It is now the default in Scanpy.

A critical hyperparameter controlling the granularity of clustering. Higher resolution values produce more, smaller clusters; lower values yield fewer, larger clusters. Optimal resolution is often determined empirically by inspecting cluster stability, marker gene specificity, and biological plausibility. Tools like clustree help visualize cluster assignments across a range of resolutions.

The mathematical objective function underlying Louvain and Leiden. Modularity quantifies the strength of division of a network into communities. It compares the fraction of edges within communities to the expected fraction if edges were distributed randomly. Maximizing this score identifies partitions where intra-community connections are denser than expected by chance, defining biologically meaningful cell groups.

A greedy modularity optimization method that partitions the k-nearest neighbor (KNN) graph into communities. It iteratively moves nodes between communities to maximize the modularity score, a measure of connection density within groups versus between groups. Louvain is computationally fast but can produce arbitrarily poorly connected communities. It remains the default in Seurat and Scanpy workflows.

An improvement over Louvain that guarantees well-connected communities by adding a refinement phase. After the initial modularity optimization, Leiden splits clusters into sub-communities before aggregation, ensuring all partitions are internally connected. This prevents the fragmentation artifacts observed in Louvain and typically yields higher-quality biological partitions. It is the recommended default for Traag et al. implementations.

A scalar metric evaluating the strength of division of a network into communities. It compares the fraction of edges within communities to the expected fraction if edges were distributed randomly. Values range from -0.5 to 1, with positive scores indicating more intra-community edges than expected by chance. Modularity is the objective function optimized by both Louvain and Leiden algorithms.

The foundational graph structure where each cell is a node connected to its k most similar cells based on a distance metric, typically Euclidean distance in PCA space. The choice of k critically influences clustering granularity: small values produce many small clusters, while large values merge distinct populations. Typical values range from 5 to 50 neighbors, often scaled relative to dataset size.

A refinement of the KNN graph where edge weights represent the Jaccard similarity between the neighborhoods of two cells. Two cells are strongly connected if they share many common neighbors, reducing noise and emphasizing robust local density relationships. The SNN graph is the standard input for Louvain and Leiden clustering in single-cell analysis pipelines.

A user-defined hyperparameter controlling the granularity of community detection. Higher resolution values produce more clusters by favoring smaller, finer partitions; lower values yield fewer, broader clusters. In Seurat, the default is 0.8, while Scanpy defaults to 1.0. Optimal resolution is typically determined by inspecting cluster stability and biological coherence rather than applying a fixed value.