Bridges

Glossary

Directed: Directed trait. The algorithm is well-defined on a directed graph.
Directed: Directed trait. The algorithm ignores the direction of the graph.
Directed: Directed trait. The algorithm does not run on a directed graph.
Undirected: Undirected trait. The algorithm is well-defined on an undirected graph.
Undirected: Undirected trait. The algorithm ignores the undirectedness of the graph.
Heterogeneous nodes: Heterogeneous nodes fully supported. The algorithm has the ability to distinguish between nodes of different types.
Heterogeneous nodes: Heterogeneous nodes allowed. The algorithm treats all selected nodes similarly regardless of their label.
Heterogeneous relationships: Heterogeneous relationships fully supported. The algorithm has the ability to distinguish between relationships of different types.
Heterogeneous relationships: Heterogeneous relationships allowed. The algorithm treats all selected relationships similarly regardless of their type.
Weighted relationships: Weighted trait. The algorithm supports a relationship property to be used as weight, specified via the relationshipWeightProperty configuration parameter.
Weighted relationships: Weighted trait. The algorithm treats each relationship as equally important, discarding the value of any relationship weight.

Introduction

Given a graph, a bridge is a relationship whose removal increases the number of connected components in the graph. Equivalently, a relationship can only be a bridge if and only if it is not contained in any cycle. The Neo4j GDS Library provides an efficient linear time sequential algorithm to compute all bridges in a graph.

For more information on this algorithm, see:

Bridge (graph theory)

Syntax

This section covers the syntax used to execute the Bridges algorithm in each of its execution modes. We are describing the named graph variant of the syntax. To learn more about general syntax variants, see Syntax overview.

Bridges syntax per mode

Run Bridges in stream mode on a named graph.

CALL gds.bridges.stream(
  graphName: String,
  configuration: Map
)
YIELD
  from: Integer,
  to: Integer

Table 1. Parameters
Name	Type	Default	Optional	Description
graphName	String	`n/a`	no	The name of a graph stored in the catalog.
configuration	Map	`{}`	yes	Configuration for algorithm-specifics and/or graph filtering.

Table 2. Configuration
Name	Type	Default	Optional	Description
nodeLabels	List of String	`['*']`	yes	Filter the named graph using the given node labels. Nodes with any of the given labels will be included.
relationshipTypes	List of String	`['*']`	yes	Filter the named graph using the given relationship types. Relationships with any of the given types will be included.
concurrency	Integer	`1`	yes	The algorithm is single-threaded and changing the concurrency parameter has no effect on the runtime.
jobId	String	`Generated internally`	yes	An ID that can be provided to more easily track the algorithm’s progress.
logProgress	Boolean	`true`	yes	If disabled the progress percentage will not be logged.

Table 3. Results
Name	Type	Description
from	Integer	Start node ID.
to	Integer	End node ID.

Examples

All the examples below should be run in an empty database.

The examples use Cypher projections as the norm. Native projections will be deprecated in a future release.

In this section we will show examples of running the Bridges algorithm on a concrete graph. The intention is to illustrate what the results look like and to provide a guide in how to make use of the algorithm in a real setting. We will do this on a small social network graph of a handful nodes connected in a particular pattern. The example graph looks like this:

The following Cypher statement will create the example graph in the Neo4j database:

CREATE
  (nAlice:User {name: 'Alice'}),
  (nBridget:User {name: 'Bridget'}),
  (nCharles:User {name: 'Charles'}),
  (nDoug:User {name: 'Doug'}),
  (nMark:User {name: 'Mark'}),
  (nMichael:User {name: 'Michael'}),

  (nAlice)-[:LINK]->(nBridget),
  (nAlice)-[:LINK]->(nCharles),
  (nCharles)-[:LINK]->(nBridget),

  (nAlice)-[:LINK]->(nDoug),

  (nMark)-[:LINK]->(nDoug),
  (nMark)-[:LINK]->(nMichael),
  (nMichael)-[:LINK]->(nDoug);

This graph has two clusters of Users, that are closely connected. Between those clusters there is one single edge.

The following statement will project a graph using a Cypher projection and store it in the graph catalog under the name 'myGraph'.

MATCH (source:User)-[r:LINK]->(target:User)
RETURN gds.graph.project(
  'myGraph',
  source,
  target,
  {},
  { undirectedRelationshipTypes: ['*'] }
)

Memory Estimation

First off, we will estimate the cost of running the algorithm using the estimate procedure. This can be done with any execution mode. We will use the stream mode in this example. Estimating the algorithm is useful to understand the memory impact that running the algorithm on your graph will have. When you later actually run the algorithm in one of the execution modes the system will perform an estimation. If the estimation shows that there is a very high probability of the execution going over its memory limitations, the execution is prohibited. To read more about this, see Automatic estimation and execution blocking.

For more details on estimate in general, see Memory Estimation.

The following will estimate the memory requirements for running the algorithm:

CALL gds.bridges.stream.estimate('myGraph', {})
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory

Table 4. Results
nodeCount	relationshipCount	bytesMin	bytesMax	requiredMemory
6	14	1040	1040	"1040 Bytes"

Stream

In the stream execution mode, the algorithm returns the bridge for each relationship. This allows us to inspect the results directly or post-process them in Cypher without any side effects.

For more details on the stream mode in general, see Stream.

The following will run the algorithm in stream mode:

CALL gds.bridges.stream('myGraph')
YIELD from, to
RETURN gds.util.asNode(from).name AS fromName, gds.util.asNode(to).name AS toName
ORDER BY fromName ASC, toName ASC

Table 5. Results
fromName	toName
"Alice"	"Doug"