Depth First Search
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
The Depth First Search algorithm is a graph traversal that starts at a given node and explores as far as possible along each branch before backtracking, see https://en.wikipedia.org/wiki/Depthfirst_search. A related algorithm is the Breadth First Search algorithm, Breadth First Search. This algorithm can be preferred over Breadth First Search for example if one wants to find a target node at a large distance and exploring a random path has decent probability of success. There are multiple termination conditions supported for the traversal, based on either reaching one of several target nodes, reaching a maximum depth, exhausting a given budget of traversed relationship cost, or just traversing the whole graph. The output of the procedure contains information about which nodes were visited and in what order.
2. Syntax
CALL gds.dfs.stream(
graphName: String,
configuration: Map
)
YIELD
sourceNode: Integer,
nodeIds: Integer,
path: Path
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 algorithm is singlethreaded and changing the concurrency parameter has no effect on the runtime. 

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. 

sourceNode 
Integer 

no 
The node id of the node where to start the traversal. 
targetNodes 
List of Integer 

yes 
Ids for target nodes. Traversal terminates when any target node is visited. 
maxDepth 
Integer 

yes 
The maximum distance from the source node at which nodes are visited. 
Name  Type  Description 

sourceNode 
Integer 
The node id of the node where to start the traversal. 
nodeIds 
List of Integer 
The ids of all nodes that were visited during the traversal. 
path 
Path 
A path containing all the nodes that were visited during the traversal. 
CALL gds.dfs.mutate(
graphName: string,
configuration: map
)
YIELD
relationshipsWritten: Integer,
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
mutateMillis: 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. 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 algorithm is singlethreaded and changing the concurrency parameter has no effect on the runtime. 

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. 

sourceNode 
Integer 

no 
The node id of the node where to start the traversal. 
targetNodes 
List of Integer 

yes 
Ids for target nodes. Traversal terminates when any target node is visited. 
maxDepth 
Integer 

yes 
The maximum distance from the source node at which nodes are visited. 
mutateRelationshipType 
String 

no 
The relationship type used for the new relationships written to the projected graph. 
Name  Type  Description 

preProcessingMillis 
Integer 
Milliseconds for preprocessing the graph. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Unused. 
mutateMillis 
Integer 
Milliseconds for adding relationships to the projected graph. 
relationshipsWritten 
Integer 
The number of relationships that were added. 
configuration 
Map 
The configuration used for running the algorithm. 
3. Examples
All the examples below should be run in an empty database. The examples use native projections as the norm, although Cypher projections can be used as well. 
In this section we will show examples of running the Depth First Search 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 graph of a handful nodes connected in a particular pattern. The example graph looks like this:
Consider the graph projected by the following Cypher statement:
CREATE
(nA:Node {name: 'A'}),
(nB:Node {name: 'B'}),
(nC:Node {name: 'C'}),
(nD:Node {name: 'D'}),
(nE:Node {name: 'E'}),
(nA)[:REL]>(nB),
(nA)[:REL]>(nC),
(nB)[:REL]>(nE),
(nC)[:REL]>(nD)
CALL gds.graph.project('myGraph', 'Node', 'REL')
In the following examples we will demonstrate using the Depth First Search algorithm on this graph.
3.1. 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.
MATCH (source:Node {name: 'A'})
CALL gds.dfs.stream.estimate('myGraph', {
sourceNode: source
})
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory
RETURN nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory
nodeCount  relationshipCount  bytesMin  bytesMax  requiredMemory 

5 
4 
352 
352 
"352 Bytes" 
3.2. Stream
In the stream
execution mode, the algorithm returns the path in traversal order for each relationship.
This allows us to inspect the results directly or postprocess them in Cypher without any side effects.
For more details on the stream
mode in general, see Stream.
MATCH (source:Node{name:'A'})
CALL gds.dfs.stream('myGraph', {
sourceNode: source
})
YIELD path
RETURN path
If we do not specify any of the options for early termination, the algorithm will traverse the entire graph:
In the image below we can see the traversal order of the nodes, marked by relationship type NEXT
:
MATCH (source:Node{name:'A'}), (d:Node{name:'D'}), (e:Node{name:'E'})
WITH source, [d, e] AS targetNodes
CALL gds.dfs.stream('myGraph', {
sourceNode: source,
targetNodes: targetNodes
})
YIELD path
RETURN path
If specifying nodes D
and E
as target nodes, not all nodes at distance 1 will be visited due to the depth first traversal order, in which node D
is reached before B
.
MATCH (source:Node{name:'A'})
CALL gds.dfs.stream('myGraph', {
sourceNode: source,
maxDepth: 1
})
YIELD path
RETURN path
In the above case, nodes D
and E
were not visited since they are at distance 2 from node A
.
3.3. Mutate
The mutate
execution mode updates the named graph with new relationships.
The path returned from the Depth First Search algorithm is a line graph, where the nodes appear in the order they were visited by the algorithm.
The relationship type has to be configured using the mutateRelationshipType
option.
The mutate
mode is especially useful when multiple algorithms are used in conjunction.
For more details on the mutate
mode in general, see Mutate.
Depth First Search mutate
supports the same early termination conditions as the stream
mode.
mutate
mode:MATCH (source:Node{name:'A'})
CALL gds.dfs.mutate('myGraph', {
sourceNode: source,
mutateRelationshipType: 'DFS'
})
YIELD relationshipsWritten
RETURN relationshipsWritten
relationshipsWritten 

4 
After executing the above query, the inmemory graph will be updated with new relationships of type DFS
.
The relationships produced are always directed, even if the input graph is undirected. 