Induced Subgraph

Overview

The Induced Subgraph algorithm extracts the subgraph formed by a given set of nodes and all edges between them. This enables focused analysis on a subset of the graph, revealing local structure and connectivity patterns among selected nodes.

Concepts

Induced Subgraph

An induced subgraph includes only the nodes from the given set and all edges that have both endpoints in that set.

As this example shows, when specifying node set S = {A, B, I, K, L, M, N}, the induced subgraph is the graph whose node set is S and whose edge set contains all edges that have both endpoints in S.

Considerations

• The algorithm respects edge direction.
• Multi-edges between the same pair of nodes are preserved.
• Self-loops are included if the node is in the specified set.

Example Graph

GQL
INSERT (A:default {_id: "A"}), (B:default {_id: "B"}),
       (C:default {_id: "C"}), (D:default {_id: "D"}),
       (E:default {_id: "E"}), (F:default {_id: "F"}),
       (G:default {_id: "G"}), (H:default {_id: "H"}),
       (I:default {_id: "I"}),
       (A)-[:default]->(B), (C)-[:default]->(A),
       (E)-[:default]->(C), (E)-[:default]->(A),
       (C)-[:default]->(D), (D)-[:default]->(A),
       (D)-[:default]->(A), (F)-[:default]->(G),
       (G)-[:default]->(G), (F)-[:default]->(I),
       (H)-[:default]->(G)

Parameters

Run Mode

Returns:

GQL
CALL algo.inducedsubgraph({
  nodes: ["A,C,D,G"]
}) YIELD sourceId, targetId, edgeExists

Result:

Stream Mode

Returns the same columns as run mode, streamed for memory efficiency.

GQL
CALL algo.inducedsubgraph.stream({
  nodes: "A,C,D,G"
}) YIELD sourceId, targetId
RETURN sourceId, targetId

Result:

Stats Mode

Returns:

GQL
CALL algo.inducedsubgraph.stats({
  nodes: "A,C,D,G"
}) YIELD nodeCount, edgeCount, density

Result: