Computes betweenness centrality for nodes in the graph.

Betweenness measures how often a node appears on shortest paths between other nodes. Higher scores indicate "bridge" or "bottleneck" functions.

Uses Brandes' algorithm (O(nm) complexity).

Parameters

• :max_nodes - Limit computation to N highest-degree nodes (default: from config, 1000)
• :normalize - Return normalized scores 0-1 (default: true)
• :directed - Treat graph as directed (default: true)

Returns

Map of node_id => betweenness_score

Examples

# Compute for all nodes (up to configured max)
betweenness_centrality()

# Compute for top 100 nodes by degree
betweenness_centrality(max_nodes: 100)

# Get raw (unnormalized) scores
betweenness_centrality(normalize: false)

Computes closeness centrality for nodes in the graph.

Closeness is the inverse of the average shortest path distance from a node to all other reachable nodes. Higher scores indicate more "central" functions.

Parameters

• :normalize - Return normalized scores 0-1 (default: true)

Returns

Map of node_id => closeness_score

Examples

# Compute closeness for all nodes
closeness_centrality()

# Get raw (unnormalized) scores
closeness_centrality(normalize: false)

Computes degree centrality for all nodes.

Returns:

• in_degree: Number of incoming edges (callers)
• out_degree: Number of outgoing edges (callees)
• total_degree: Sum of in and out degree

Detects communities in the graph using the Louvain method.

The Louvain algorithm iteratively optimizes modularity to discover communities. It naturally produces a hierarchy through aggregation phases.

Parameters

• :max_iterations - Maximum optimization iterations (default: 10)
• :min_improvement - Minimum modularity improvement to continue (default: 0.0001)
• :resolution - Resolution parameter for multi-scale detection (default: 1.0)
• :hierarchical - Return hierarchical community structure (default: false)

Returns

• When :hierarchical is false: Map of community_id => [node_ids]
• When :hierarchical is true: Map with :communities, :hierarchy, :modularity_per_level

Examples

# Detect communities
detect_communities()

# Get hierarchical structure
detect_communities(hierarchical: true)

# Adjust resolution for finer/coarser communities
detect_communities(resolution: 0.5)

Detects communities using label propagation algorithm.

Fast alternative to Louvain. Each node adopts the most common label among neighbors. Converges quickly but results can be non-deterministic.

Parameters

• :max_iterations - Maximum iterations (default: 20)
• :seed - Random seed for deterministic results (optional)

Returns

Map of community_id => [node_ids]

Examples

# Detect communities with label propagation
detect_communities_lp()

# With deterministic seed
detect_communities_lp(seed: 42)

Exports the graph in D3.js force-directed JSON format.

Parameters

• :include_communities - Include community metadata (default: true)
• :max_nodes - Maximum nodes to include (default: from config, 500)

Returns

{:ok, json_map} or {:error, reason}

Examples

# Export for D3.js visualization
{:ok, json} = export_d3_json()
File.write!("graph.json", Jason.encode!(json))

Exports the graph in Graphviz DOT format.

Parameters

• :include_communities - Include community clustering (default: true)
• :color_by - Centrality metric for node coloring: :pagerank, :betweenness, :degree (default: :pagerank)
• :max_nodes - Maximum nodes to include (default: from config, 500)

Returns

{:ok, dot_string} or {:error, reason}

Examples

# Export with default settings
{:ok, dot} = export_graphviz()

# Color by betweenness centrality
{:ok, dot} = export_graphviz(color_by: :betweenness)

Finds all paths between two nodes up to a maximum depth.

Parameters

• from: Source node ID
• to: Target node ID
• opts: Keyword list of options
  • :max_depth - Maximum path length in edges (default: 10)
  • :max_paths - Maximum number of paths to return (default: 100)
  • :warn_dense - Emit warnings for dense graphs (default: true)

Returns

List of paths, where each path is a list of node IDs. Returns up to max_paths paths to prevent hangs on dense graphs.

Examples

# Find up to 100 paths with max depth of 10
find_paths(from, to)

# Find up to 50 paths with max depth of 5
find_paths(from, to, max_depth: 5, max_paths: 50)

# Disable warnings for dense graphs
find_paths(from, to, warn_dense: false)

Computes comprehensive graph statistics.

Returns a map with:

• Node counts by type
• Edge counts
• Average degree
• Density
• Connected components count
• Top nodes by PageRank

Computes PageRank scores for all nodes in the graph.

PageRank measures the importance of nodes based on incoming edges. Higher scores indicate more "important" functions/modules (those called by many others).

Parameters

• damping_factor: Probability of following an edge (default: 0.85)
• max_iterations: Maximum iterations (default: 100)
• tolerance: Convergence threshold (default: 0.0001)

Returns

Map of node_id => pagerank_score