Minimum Weight kSpanning Tree
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.
1. Introduction
Sometimes, we might require a spanning tree(a tree where its nodes are connected with each via a single path) that does not necessarily span all nodes in the graph.
The KSpanning tree heuristic algorithm returns a tree with k
nodes and k − 1
relationships.
Our heuristic processes the result found by Prim’s algorithm for the Minimum Weight Spanning Tree problem.
Like Prim, it starts from a given source node, finds a spanning tree for all nodes and then removes nodes using heuristics to produce a tree with 'k' nodes.
Note that the source node will not be necessarily included in the final output as the heuristic tries to find a globally good tree.
2. Considerations
The Minimum weight kSpanning Tree is NPHard. The algorithm in the Neo4j GDS Library is therefore not guaranteed to find the optimal answer, but should hopefully return a good approximation in practice.
Like Prim algorithm, the algorithm focuses only on the component of the source node. If that component has fewer than k
nodes, it will not look into other components, but will instead return the component.
3. Syntax
This section covers the syntax used to execute the kSpanning Tree heuristic 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.
CALL gds.alpha.kSpanningTree.write(
graphName: String,
configuration: Map
)
YIELD effectiveNodeCount: Integer,
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
writeMillis: Integer,
configuration: Map
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. 

List of String 

yes 
Filter the named graph using the given relationship types. 

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. 

Integer 

yes 
The number of concurrent threads used for writing the result to Neo4j. 

String 

no 
The node property in the Neo4j database to which the spanning tree is written. 

k 
Number 

no 
The size of the tree to be returned 
sourceNode 
Integer 

n/a 
The starting source node ID. 
String 

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

objective 
String 

yes 
If specified, the parameter dictates whether to seek a minimum or the maximum weight kspanning tree. By default, the procedure looks for a minimum weight kspanning tree. Permitted values are 'minimum' and 'maximum'. 
Name  Type  Description 

effectiveNodeCount 
Integer 
The number of visited nodes. 
preProcessingMillis 
Integer 
Milliseconds for preprocessing the data. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Milliseconds for postprocessing results of the algorithm. 
writeMillis 
Integer 
Milliseconds for writing result data back. 
configuration 
Map 
The configuration used for running the algorithm. 
4. Minimum Weight kSpanning Tree algorithm examples
In this section we will show examples of running the kSpanning Tree heuristic 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 road network graph of a handful nodes connected in a particular pattern. The example graph looks like this:
CREATE (a:Place {id: 'A'}),
(b:Place {id: 'B'}),
(c:Place {id: 'C'}),
(d:Place {id: 'D'}),
(e:Place {id: 'E'}),
(f:Place {id: 'F'}),
(g:Place {id: 'G'}),
(d)[:LINK {cost:4}]>(b),
(d)[:LINK {cost:6}]>(e),
(b)[:LINK {cost:1}]>(a),
(b)[:LINK {cost:3}]>(c),
(a)[:LINK {cost:2}]>(c),
(c)[:LINK {cost:5}]>(e),
(f)[:LINK {cost:1}]>(g);
CALL gds.graph.project(
'graph',
'Place',
{
LINK: {
properties: 'cost',
orientation: 'UNDIRECTED'
}
}
)
5. KSpanning tree examples
5.1. Minimum KSpanning Tree example
In our sample graph we have 7 nodes.
By setting the k=3
, we define that we want to find a 3minimum spanning tree that covers 3 nodes and has 2 relationships.
MATCH (n:Place{id: 'A'})
CALL gds.alpha.kSpanningTree.write('graph', {
k: 3,
sourceNode: id(n),
relationshipWeightProperty: 'cost',
writeProperty:'kmin'
})
YIELD preProcessingMillis, computeMillis, writeMillis, effectiveNodeCount
RETURN preProcessingMillis,computeMillis,writeMillis, effectiveNodeCount;
MATCH (n)
WITH n.kmin AS p, count(n) AS c
WHERE c = 3
MATCH (n)
WHERE n.kmin = p
RETURN n.id As Place, p as Partition
Place  Partition 

"A" 
0 
"B" 
0 
"C" 
0 
Nodes A, B, and C form the discovered 3minimum spanning tree of our graph.
5.2. Maximum KSpanning Tree example
MATCH (n:Place{id: 'D'})
CALL gds.alpha.kSpanningTree.write('graph', {
k: 3,
sourceNode: id(n),
relationshipWeightProperty: 'cost',
writeProperty:'kmax',
objective: 'maximum'
})
YIELD preProcessingMillis, computeMillis, writeMillis, effectiveNodeCount
RETURN preProcessingMillis,computeMillis,writeMillis, effectiveNodeCount;
MATCH (n)
WITH n.kmax AS p, count(n) AS c
WHERE c = 3
MATCH (n)
WHERE n.kmax = p
RETURN n.id As Place, p as Partition
Place  Partition 

"C" 
3 
"D" 
3 
"E" 
3 
Nodes C, D, and E form a 3maximum spanning tree of our graph.
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