# bridges

A bridge in the graph can be described as an relationship which if deleted,
creates two disjoint graph components. This algorithm finds bridges within the
graph. It has various practical usages such as road or internet network design
planning. A bridge can represent a bottleneck for many scenarios and it is
valuable to detect it on time.

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

## Procedures

> **Info**
>
> You can execute this algorithm on [graph projections, subgraphs or portions of the graph](https://memgraph.com/docs/advanced-algorithms/run-algorithms#run-procedures-on-subgraph).

### `get()`

The procedure identifies a bridge relationship in the graph which if deleted,
creates two disjoint graph components. 

#### Input:

- `subgraph: Graph` (**OPTIONAL**) ➡ A specific subgraph, which is an [object of type Graph](https://memgraph.com/docs/advanced-algorithms/run-algorithms#run-procedures-on-subgraph) returned by the `project()` function, on which the algorithm is run. 
If subgraph is not specified, the algorithm is computed on the entire graph by default.

#### Output:

* `node_from: Vertex` ➡ Represents the first node in a bridge relationship.
* `node_to: Vertex` ➡ Represents the second node in a bridge relationship.

#### Usage:

To identify a bridge relationship in agraph, use the following query: 

```cypher
CALL bridges.get()
YIELD node_from, node_to;
```

## Example

### Database state
 

The database contains the following data: 

![](https://memgraph.com/docs/pages/advanced-algorithms/available-algorithms/bridges/bridges-1.png)

Created with the following Cypher queries:

```cypher
MERGE (a:Node {id: 1}) MERGE (b:Node {id: 0}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 0}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 2}) MERGE (b:Node {id: 1}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 0}) MERGE (b:Node {id: 3}) CREATE (a)-[:RELATION]->(b);
MERGE (a:Node {id: 3}) MERGE (b:Node {id: 4}) CREATE (a)-[:RELATION]->(b);
```

### Identify bridge relationships
 

Get the values using the following query:

```cypher
CALL bridges.get() YIELD node_from, node_to
WITH node_from, node_to
MATCH (node_from)-[bridge]-(node_to)
RETURN bridge, node_from, node_to;
```

Results:

```plaintext
+-----------------+-----------------+-----------------+
| bridge          | node_from       | node_to         |
+-----------------+-----------------+-----------------+
| [:RELATION]     | (:Node {id: 3}) | (:Node {id: 4}) |
| [:RELATION]     | (:Node {id: 0}) | (:Node {id: 3}) |
+-----------------+-----------------+-----------------+
```