biconnected_components

Finding biconnected components means finding a maximal biconnected subgraph. Subgraph is biconnected if:

it is possible to go from each node to another within a biconnected subgraph,
the first scenario remains true even after removing any node from the subgraph.

The algorithm works by finding articulation points, and then traversing from these articulation points toward other nodes, which all together form one biconnected component.

Source code

Trait	Value
Module type	algorithm
Implementation	C++
Graph direction	undirected
Edge weights	unweighted
Parallelism	sequential

Procedures

You can execute this algorithm on graph projections, subgraphs or portions of the graph.

`get()`

Output:

bcc_id: integer ➡ Biconnected component identifier. There is no order of nodes within one biconnected component.
node_from: Vertex ➡ First node of a relationship contained in biconnected component.
node_to: Vertex ➡ Second node of a relationship contained in biconnected component

Usage:

CALL biconnected_components.get()
YIELD bcc_id, node_from, node_to;

Example

Database state

The database contains the following data:

Add new data

New data is added to the database:

MERGE (a:Node {id: 0}) MERGE (b:Node {id: 1}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 1}) MERGE (b:Node {id: 2}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 1}) MERGE (b:Node {id: 3}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 3}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 4}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 3}) MERGE (b:Node {id: 4}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 1}) MERGE (b:Node {id: 5}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 0}) MERGE (b:Node {id: 6}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 5}) MERGE (b:Node {id: 6}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 5}) MERGE (b:Node {id: 7}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 5}) MERGE (b:Node {id: 8}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 7}) MERGE (b:Node {id: 8}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 8}) MERGE (b:Node {id: 9}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 10}) MERGE (b:Node {id: 11}) CREATE (a)-[:RELATION]->(b);

Find biconnected componentes

Get the values using the following query:

CALL biconnected_components.get()
YIELD bcc_id, node_from, node_to
WITH bcc_id, node_from, node_to
MATCH (node_from)-[relationship]-(node_to)
RETURN bcc_id, relationship, node_from, node_to;

Results:

+------------------+------------------+------------------+------------------+
| bcc_id           | relationship     | node_from        | node_to          |
+------------------+------------------+------------------+------------------+
| 0                | [:RELATION]      | (:Node {id: 2})  | (:Node {id: 4})  |
| 0                | [:RELATION]      | (:Node {id: 3})  | (:Node {id: 4})  |
| 0                | [:RELATION]      | (:Node {id: 1})  | (:Node {id: 3})  |
| 0                | [:RELATION]      | (:Node {id: 2})  | (:Node {id: 3})  |
| 0                | [:RELATION]      | (:Node {id: 1})  | (:Node {id: 2})  |
| 1                | [:RELATION]      | (:Node {id: 8})  | (:Node {id: 9})  |
| 2                | [:RELATION]      | (:Node {id: 5})  | (:Node {id: 8})  |
| 2                | [:RELATION]      | (:Node {id: 7})  | (:Node {id: 8})  |
| 2                | [:RELATION]      | (:Node {id: 5})  | (:Node {id: 7})  |
| 3                | [:RELATION]      | (:Node {id: 0})  | (:Node {id: 6})  |
| 3                | [:RELATION]      | (:Node {id: 5})  | (:Node {id: 6})  |
| 3                | [:RELATION]      | (:Node {id: 1})  | (:Node {id: 5})  |
| 3                | [:RELATION]      | (:Node {id: 0})  | (:Node {id: 1})  |
| 4                | [:RELATION]      | (:Node {id: 10}) | (:Node {id: 11}) |
+------------------+------------------+------------------+------------------+