All Pairs Shortest Path
The All Pairs Shortest Path (APSP) calculates the shortest (weighted) path between all pairs of nodes. This algorithm has optimizations that make it quicker than calling the Single Source Shortest Path algorithm for every pair of nodes in the graph.
This feature is in the alpha tier. For more information on feature tiers, see API Tiers.
Glossary
 Directed

Directed trait. The algorithm is welldefined 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 welldefined 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.
History and explanation
Some pairs of nodes might not be reachable between each other, so no shortest path exists between these pairs.
In this scenario, the algorithm will return Infinity
value as a result between these pairs of nodes.
GDS includes functions such as gds.util.isFinite
to help filter infinity values from results.
Starting with Neo4j 5, the Infinity
literal is now included in Cypher too.
Usecases  when to use the All Pairs Shortest Path algorithm

The All Pairs Shortest Path algorithm is used in urban service system problems, such as the location of urban facilities or the distribution or delivery of goods. One example of this is determining the traffic load expected on different segments of a transportation grid. For more information, see Urban Operations Research.

All pairs shortest path is used as part of the REWIRE data center design algorithm that finds a network with maximum bandwidth and minimal latency. There are more details about this approach in "REWIRE: An Optimizationbased Framework for Data Center Network Design"
Syntax
CALL gds.allShortestPaths.stream(
graphName: string,
configuration: map
)
YIELD sourceNodeId, targetNodeId, distance
Name  Type  Default  Optional  Description 

graphName 
String 

no 
The name of a graph stored in the catalog. 
configuration 
Map 

yes 
Configuration for algorithmspecifics and/or graph filtering. 
Name  Type  Default  Optional  Description 

List of String 

yes 
Filter the named graph using the given node labels. Nodes with any of the given labels will be included. 

List of String 

yes 
Filter the named graph using the given relationship types. Relationships with any of the given types will be included. 

Integer 

yes 
The number of concurrent threads used for running the algorithm. 

String 

yes 
An ID that can be provided to more easily track the algorithm’s progress. 

Boolean 

yes 
If disabled the progress percentage will not be logged. 

String 

yes 
Name of the relationship property to use as weights. If unspecified, the algorithm runs unweighted. 
Name  Type  Description 

sourceNodeId 
Integer 
The source node. 
targetNodeId 
Integer 
The target node. 
distance 
Float 
The distance of the shortest path from source to target. 
All Pairs Shortest Path algorithm sample
CREATE (a:Loc {name: 'A'}),
(b:Loc {name: 'B'}),
(c:Loc {name: 'C'}),
(d:Loc {name: 'D'}),
(e:Loc {name: 'E'}),
(f:Loc {name: 'F'}),
(a)[:ROAD {cost: 50}]>(b),
(a)[:ROAD {cost: 50}]>(c),
(a)[:ROAD {cost: 100}]>(d),
(b)[:ROAD {cost: 40}]>(d),
(c)[:ROAD {cost: 40}]>(d),
(c)[:ROAD {cost: 80}]>(e),
(d)[:ROAD {cost: 30}]>(e),
(d)[:ROAD {cost: 80}]>(f),
(e)[:ROAD {cost: 40}]>(f);
Using native projection
CALL gds.graph.project(
'nativeGraph',
'Loc',
{
ROAD: {
properties: 'cost'
}
}
)
YIELD graphName
CALL gds.allShortestPaths.stream('nativeGraph', {
relationshipWeightProperty: 'cost'
})
YIELD sourceNodeId, targetNodeId, distance
WITH sourceNodeId, targetNodeId, distance
WHERE gds.util.isFinite(distance) = true
WITH gds.util.asNode(sourceNodeId) AS source, gds.util.asNode(targetNodeId) AS target, distance WHERE source <> target
RETURN source.name AS source, target.name AS target, distance
ORDER BY distance DESC, source ASC, target ASC
LIMIT 10
source  target  distance 

"A" 
"F" 
160 
"A" 
"E" 
120 
"B" 
"F" 
110 
"C" 
"F" 
110 
"A" 
"D" 
90 
"B" 
"E" 
70 
"C" 
"E" 
70 
"D" 
"F" 
70 
"A" 
"B" 
50 
"A" 
"C" 
50 
This query returned the top 10 pairs of nodes that are the furthest away from each other. F and E appear to be quite distant from the others.
Using Cypher projection
MATCH (src:Loc)[r:ROAD]>(trg:Loc)
RETURN gds.graph.project(
'cypherGraph',
src,
trg,
{relationshipType: type(r), relationshipProperties: {cost: r.cost}},
{undirectedRelationshipTypes: ['ROAD']
})
CALL gds.allShortestPaths.stream('cypherGraph', {
relationshipWeightProperty: 'cost'
})
YIELD sourceNodeId, targetNodeId, distance
WITH sourceNodeId, targetNodeId, distance
WHERE gds.util.isFinite(distance) = true
WITH gds.util.asNode(sourceNodeId) AS source, gds.util.asNode(targetNodeId) AS target, distance WHERE source <> target
RETURN source.name AS source, target.name AS target, distance
ORDER BY distance DESC, source ASC, target ASC
LIMIT 10
source  target  distance 

"A" 
"F" 
160 
"F" 
"A" 
160 
"A" 
"E" 
120 
"E" 
"A" 
120 
"B" 
"F" 
110 
"C" 
"F" 
110 
"F" 
"B" 
110 
"F" 
"C" 
110 
"A" 
"D" 
90 
"D" 
"A" 
90 