Graph Algorithms Reference

GraphQLite provides 18 built-in graph algorithms accessible via Cypher functions, the Python Graph API, and the Rust Graph API.

For guidance on choosing the right algorithm for your use case, see Using Graph Algorithms.

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PageRank

Cypher

CALL pageRank([damping, iterations]) YIELD node, score

Python

graph.pagerank(damping=0.85, iterations=20)

Rust

graph.pagerank(damping: f64, iterations: usize) -> Result<Vec<PageRankResult>>

Parameters

Parameter	Type	Default	Description
damping	Float	0.85	Damping factor
iterations	Integer	20	Number of power iterations

Return shape

Python: list[dict] with keys node_id, user_id, score

Rust: Vec<PageRankResult> — fields: node_id: i64, user_id: String, score: f64

Complexity: O(iterations × (V + E))

Example

results = graph.pagerank(damping=0.85, iterations=30)
for r in sorted(results, key=lambda x: x['score'], reverse=True)[:5]:
    print(r['user_id'], r['score'])

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Degree Centrality

Cypher

CALL degreeCentrality() YIELD node, in_degree, out_degree, degree

Python

graph.degree_centrality()

Rust

graph.degree_centrality() -> Result<Vec<DegreeCentralityResult>>

Parameters: none

Return shape

Python: list[dict] with keys node_id, user_id, in_degree, out_degree, degree

Rust: Vec<DegreeCentralityResult> — fields: node_id: i64, user_id: String, in_degree: usize, out_degree: usize, degree: usize

Complexity: O(V + E)

Example

for r in graph.degree_centrality():
    print(r['user_id'], 'in:', r['in_degree'], 'out:', r['out_degree'])

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Betweenness Centrality

Cypher

CALL betweennessCentrality() YIELD node, score

Python

graph.betweenness_centrality()

Rust

graph.betweenness_centrality() -> Result<Vec<BetweennessCentralityResult>>

Parameters: none

Return shape

Python: list[dict] with keys node_id, user_id, score

Rust: Vec<BetweennessCentralityResult> — fields: node_id: i64, user_id: String, score: f64

Complexity: O(V × E)

Example

results = graph.betweenness_centrality()

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Closeness Centrality

Cypher

CALL closenessCentrality() YIELD node, score

Python

graph.closeness_centrality()

Rust

graph.closeness_centrality() -> Result<Vec<ClosenessCentralityResult>>

Parameters: none

Return shape

Python: list[dict] with keys node_id, user_id, score

Rust: Vec<ClosenessCentralityResult> — fields: node_id: i64, user_id: String, score: f64

Complexity: O(V × (V + E))

Example

results = graph.closeness_centrality()

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Eigenvector Centrality

Cypher

CALL eigenvectorCentrality([iterations]) YIELD node, score

Python

graph.eigenvector_centrality(iterations=100)

Rust

graph.eigenvector_centrality(iterations: usize) -> Result<Vec<EigenvectorCentralityResult>>

Parameters

Parameter	Type	Default	Description
iterations	Integer	100	Power iteration count

Return shape

Python: list[dict] with keys node_id, user_id, score

Rust: Vec<EigenvectorCentralityResult> — fields: node_id: i64, user_id: String, score: f64

Complexity: O(iterations × E)

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Louvain Community Detection

Cypher

CALL louvain([resolution]) YIELD node, community

Python

graph.louvain(resolution=1.0)

Rust

graph.louvain(resolution: f64) -> Result<Vec<CommunityResult>>

Parameters

Parameter	Type	Default	Description
resolution	Float	1.0	Resolution parameter controlling community granularity

Return shape

Python: list[dict] with keys node_id, user_id, community

Rust: Vec<CommunityResult> — fields: node_id: i64, user_id: String, community: i64

Example

communities = graph.louvain(resolution=0.5)

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Leiden Community Detection

Python only

graph.leiden_communities(resolution=1.0, random_seed=None)

Parameters

Parameter	Type	Default	Description
resolution	Float	1.0	Resolution parameter
random_seed	Integer | None	None	Seed for reproducibility

Return shape: list[dict] with keys node_id, user_id, community

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Label Propagation

Cypher

CALL labelPropagation([iterations]) YIELD node, community

Python

graph.community_detection(iterations=10)

Rust

graph.community_detection(iterations: usize) -> Result<Vec<CommunityResult>>

Parameters

Parameter	Type	Default	Description
iterations	Integer	10	Maximum iterations

Return shape

Python: list[dict] with keys node_id, user_id, community

Rust: Vec<CommunityResult> — fields: node_id: i64, user_id: String, community: i64

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Weakly Connected Components

Cypher

CALL weaklyConnectedComponents() YIELD node, component

Python

graph.weakly_connected_components()

Rust

graph.weakly_connected_components() -> Result<Vec<ComponentResult>>

Parameters: none

Return shape

Python: list[dict] with keys node_id, user_id, component

Rust: Vec<ComponentResult> — fields: node_id: i64, user_id: String, component: i64

Complexity: O(V + E)

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Strongly Connected Components

Cypher

CALL stronglyConnectedComponents() YIELD node, component

Python

graph.strongly_connected_components()

Rust

graph.strongly_connected_components() -> Result<Vec<ComponentResult>>

Parameters: none

Return shape

Python: list[dict] with keys node_id, user_id, component

Rust: Vec<ComponentResult> — fields: node_id: i64, user_id: String, component: i64

Complexity: O(V + E) (Tarjan or Kosaraju)

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Shortest Path

Cypher (path function)

MATCH p = shortestPath((a)-[*]->(b))
RETURN p

Cypher (Dijkstra)

CALL dijkstra(source, target[, weight_property]) YIELD path, distance

Python

graph.shortest_path(source, target, weight_property=None)

Rust

graph.shortest_path(source: &str, target: &str, weight_property: Option<&str>) -> Result<ShortestPathResult>

Parameters

Parameter	Type	Default	Description
source	String	required	Source node user ID
target	String	required	Target node user ID
weight_property	String | None	None	Edge property to use as weight; unweighted BFS if None

Return shape

Python: dict with keys path (list of user IDs), distance (float), found (bool)

Rust: ShortestPathResult — fields: path: Vec<String>, distance: f64, found: bool

Example

result = graph.shortest_path('alice', 'bob', weight_property='cost')
if result['found']:
    print(result['path'], result['distance'])

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A* (A-Star)

Cypher

CALL astar(source, target[, lat_prop, lon_prop]) YIELD path, distance

Python

graph.astar(source, target, lat_prop=None, lon_prop=None)

Rust

graph.astar(source: &str, target: &str, lat_prop: Option<&str>, lon_prop: Option<&str>) -> Result<AStarResult>

Parameters

Parameter	Type	Default	Description
source	String	required	Source node user ID
target	String	required	Target node user ID
lat_prop	String | None	None	Node property for latitude
lon_prop	String | None	None	Node property for longitude

Return shape

Python: dict with keys path, distance, found, nodes_explored

Rust: AStarResult — fields: path: Vec<String>, distance: f64, found: bool, nodes_explored: usize

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All-Pairs Shortest Path

Cypher

CALL apsp() YIELD source, target, distance

Python

graph.all_pairs_shortest_path()

Rust

graph.all_pairs_shortest_path() -> Result<Vec<ApspResult>>

Parameters: none

Return shape

Python: list[dict] with keys source, target, distance

Rust: Vec<ApspResult> — fields: source: String, target: String, distance: f64

Complexity: O(V × (V + E))

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BFS (Breadth-First Search)

Cypher

CALL bfs(start[, max_depth]) YIELD node, depth, order

Python

graph.bfs(start, max_depth=-1)

Rust

graph.bfs(start: &str, max_depth: i64) -> Result<Vec<TraversalResult>>

Parameters

Parameter	Type	Default	Description
start	String	required	Starting node user ID
max_depth	Integer	-1	Maximum depth; -1 means unlimited

Return shape

Python: list[dict] with keys user_id, depth, order

Rust: Vec<TraversalResult> — fields: user_id: String, depth: usize, order: usize

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DFS (Depth-First Search)

Cypher

CALL dfs(start[, max_depth]) YIELD node, depth, order

Python

graph.dfs(start, max_depth=-1)

Rust

graph.dfs(start: &str, max_depth: i64) -> Result<Vec<TraversalResult>>

Parameters

Parameter	Type	Default	Description
start	String	required	Starting node user ID
max_depth	Integer	-1	Maximum depth; -1 means unlimited

Return shape: same as BFS — list[dict] / Vec<TraversalResult> with user_id, depth, order

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Node Similarity

Cypher

CALL nodeSimilarity([node1, node2, threshold, top_k]) YIELD node1, node2, similarity

Python

graph.node_similarity(node1_id=None, node2_id=None, threshold=0.0, top_k=0)

Rust

graph.node_similarity(node1_id: Option<i64>, node2_id: Option<i64>, threshold: f64, top_k: usize) -> Result<Vec<NodeSimilarityResult>>

Parameters

Parameter	Type	Default	Description
node1_id	Integer | None	None	Fix first node; None means all pairs
node2_id	Integer | None	None	Fix second node; None means all pairs
threshold	Float	0.0	Minimum similarity to include
top_k	Integer	0	Return at most top_k results; 0 means all

Algorithm: Jaccard similarity based on shared neighbors.

Limits: with threshold > 0 only pairs that share at least one neighbor can qualify, so candidates are enumerated through shared neighbors and graphs up to 50,000 nodes are accepted. With threshold = 0 every pair (including similarity 0.0) is part of the result, which is O(N²) by definition, so all-pairs mode is capped at 5,000 nodes; use a threshold, top_k, or the specific-pair form above that.

Return shape

Python: list[dict] with keys node1, node2, similarity

Rust: Vec<NodeSimilarityResult> — fields: node1: String, node2: String, similarity: f64

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KNN (k-Nearest Neighbors)

Cypher

CALL knn(node, k) YIELD neighbor, similarity, rank

Python

graph.knn(node_id, k=10)

Rust

graph.knn(node_id: i64, k: usize) -> Result<Vec<KnnResult>>

Parameters

Parameter	Type	Default	Description
node_id	Integer	required	Source node internal ID
k	Integer	10	Number of neighbors to return

Return shape

Python: list[dict] with keys neighbor, similarity, rank

Rust: Vec<KnnResult> — fields: neighbor: String, similarity: f64, rank: usize

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Triangle Count

Cypher

CALL triangleCount() YIELD node, triangles, clustering_coefficient

Python

graph.triangle_count()

Rust

graph.triangle_count() -> Result<Vec<TriangleCountResult>>

Parameters: none

Return shape

Python: list[dict] with keys node_id, user_id, triangles, clustering_coefficient

Rust: Vec<TriangleCountResult> — fields: node_id: i64, user_id: String, triangles: usize, clustering_coefficient: f64

Complexity: O(V × degree²)

Example

for r in graph.triangle_count():
    print(r['user_id'], r['triangles'], r['clustering_coefficient'])