Degree Centrality
Glossary
 Directed

Directed trait. The algorithm is welldefined on a directed graph.
 Undirected

Undirected trait. The algorithm is welldefined on an undirected graph.
 Homogeneous

Homogeneous trait. The algorithm will treat all nodes and relationships in its input graph(s) similarly, as if they were all of the same type. If multiple types of nodes or relationships exist in the graph, this must be taken into account when analysing the results of the algorithm.
 Heterogeneous

Heterogeneous trait. The algorithm has the ability to distinguish between nodes and/or relationships of different types.
 Weighted

Weighted trait. The algorithm supports configuration to set node and/or relationship properties to use as weights. These values can represent cost, time, capacity or some other domainspecific properties, specified via the nodeWeightProperty, nodeProperties and relationshipWeightProperty configuration parameters. The algorithm will by default consider each node and/or relationship as equally important.
1. Introduction
The Degree Centrality algorithm can be used to find popular nodes within a graph. Degree centrality measures the number of incoming or outgoing (or both) relationships from a node, depending on the orientation of a relationship projection. For more information on relationship orientations, see the relationship projection syntax section.
It can be applied to either weighted or unweighted graphs. In the weighted case the algorithm computes the sum of all positive weights of adjacent relationships of a node, for each node in the graph. Nonpositive weights are ignored.
It can be applied to heterogenous graphs, however the algorithm will not calculate degree centrality per relationship type. Instead it will treat the graph as homogenous, as indicated by the algorithm traits.
For more information on this algorithm, see:
2. Usecases
The Degree Centrality algorithm has been shown to be useful in many different applications. For example:

Degree centrality is an important component of any attempt to determine the most important people in a social network. For example, in BrandWatch’s most influential men and women on Twitter 2017 the top 5 people in each category have over 40m followers each, which is a lot higher than the average degree.

Weighted degree centrality has been used to help separate fraudsters from legitimate users of an online auction. The weighted centrality for fraudsters is significantly higher because they tend to collude with each other to artificially increase the price of items. Read more in Two Step graphbased semisupervised Learning for Online Auction Fraud Detection
3. Syntax
This section covers the syntax used to execute the Degree Centrality 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.degree.stream(
graphName: String,
configuration: Map
) YIELD
nodeId: Integer,
score: Float
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. 

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. 

orientation 
String 

yes 
The orientation used to compute node degrees. Supported orientations are 
String 

yes 
Name of the relationship property to use for weighted degree computation. If unspecified, the algorithm runs unweighted. 
Name  Type  Description 

nodeId 
Integer 
Node ID. 
score 
Float 
Degree Centrality score. 
CALL gds.degree.stats(
graphName: String,
configuration: Map
) YIELD
centralityDistribution: Map,
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: 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. 

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. 

orientation 
String 

yes 
The orientation used to compute node degrees. Supported orientations are 
String 

yes 
Name of the relationship property to use for weighted degree computation. If unspecified, the algorithm runs unweighted. 
Name  Type  Description 

centralityDistribution 
Map 
Map containing min, max, mean as well as p50, p75, p90, p95, p99 and p999 percentile values of centrality values. 
preProcessingMillis 
Integer 
Milliseconds for preprocessing the graph. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Milliseconds for computing the statistics. 
configuration 
Map 
Configuration used for running the algorithm. 
CALL gds.degree.mutate(
graphName: String,
configuration: Map
) YIELD
centralityDistribution: Map,
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
mutateMillis: Integer,
nodePropertiesWritten: 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 

mutateProperty 
String 

no 
The node property in the GDS graph to which the degree centrality is written. 
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. 

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. 

orientation 
String 

yes 
The orientation used to compute node degrees. Supported orientations are 
String 

yes 
Name of the relationship property to use for weighted degree computation. If unspecified, the algorithm runs unweighted. 
Name  Type  Description 

centralityDistribution 
Map 
Map containing min, max, mean as well as p50, p75, p90, p95, p99 and p999 percentile values of centrality values. 
preProcessingMillis 
Integer 
Milliseconds for preprocessing the graph. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Milliseconds for computing the statistics. 
mutateMillis 
Integer 
Milliseconds for adding properties to the projected graph. 
nodePropertiesWritten 
Integer 
Number of properties added to the projected graph. 
configuration 
Map 
Configuration used for running the algorithm. 
CALL gds.degree.write(
graphName: String,
configuration: Map
) YIELD
centralityDistribution: Map,
preProcessingMillis: Integer,
computeMillis: Integer,
postProcessingMillis: Integer,
writeMillis: Integer,
nodePropertiesWritten: 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. 

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. 

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 degree centrality is written. 

orientation 
String 

yes 
The orientation used to compute node degrees. Supported orientations are 
String 

yes 
Name of the relationship property to use for weighted degree computation. If unspecified, the algorithm runs unweighted. 
Name  Type  Description 

centralityDistribution 
Map 
Map containing min, max, mean as well as p50, p75, p90, p95, p99 and p999 percentile values of centrality values. 
preProcessingMillis 
Integer 
Milliseconds for preprocessing the graph. 
computeMillis 
Integer 
Milliseconds for running the algorithm. 
postProcessingMillis 
Integer 
Milliseconds for computing the statistics. 
writeMillis 
Integer 
Milliseconds for writing result data back. 
nodePropertiesWritten 
Integer 
Number of properties written to Neo4j. 
configuration 
Map 
The configuration used for running the algorithm. 
4. Examples
In this section we will show examples of running the Degree Centrality 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:
CREATE
(alice:User {name: 'Alice'}),
(bridget:User {name: 'Bridget'}),
(charles:User {name: 'Charles'}),
(doug:User {name: 'Doug'}),
(mark:User {name: 'Mark'}),
(michael:User {name: 'Michael'}),
(alice)[:FOLLOWS {score: 1}]>(doug),
(alice)[:FOLLOWS {score: 2}]>(bridget),
(alice)[:FOLLOWS {score: 5}]>(charles),
(mark)[:FOLLOWS {score: 1.5}]>(doug),
(mark)[:FOLLOWS {score: 4.5}]>(michael),
(bridget)[:FOLLOWS {score: 1.5}]>(doug),
(charles)[:FOLLOWS {score: 2}]>(doug),
(michael)[:FOLLOWS {score: 1.5}]>(doug)
With the graph in Neo4j we can now project it into the graph catalog to prepare it for algorithm execution.
We do this using a native projection targeting the User
nodes and the FOLLOWS
relationships.
In the examples below we will use named graphs and native projections as the norm. However, Cypher projections can also be used. 
CALL gds.graph.project(
'myGraph',
'User',
{
FOLLOWS: {
orientation: 'REVERSE',
properties: ['score']
}
}
)
The graph is projected in a REVERSE
orientation in order to retrieve people with the most followers in the following examples.
This will be demonstrated using the Degree Centrality algorithm on this graph.
4.1. 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 write
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.
CALL gds.degree.write.estimate('myGraph', { writeProperty: 'degree' })
YIELD nodeCount, relationshipCount, bytesMin, bytesMax, requiredMemory
nodeCount  relationshipCount  bytesMin  bytesMax  requiredMemory 

6 
8 
32 
32 
"32 Bytes" 
4.2. Stream
In the stream
execution mode, the algorithm returns the degree centrality for each node.
This allows us to inspect the results directly or postprocess them in Cypher without any side effects.
For example, we can order the results to find the nodes with the highest degree centrality.
For more details on the stream
mode in general, see Stream.
stream
mode:CALL gds.degree.stream('myGraph')
YIELD nodeId, score
RETURN gds.util.asNode(nodeId).name AS name, score AS followers
ORDER BY followers DESC, name DESC
name  followers 

"Doug" 
5.0 
"Michael" 
1.0 
"Charles" 
1.0 
"Bridget" 
1.0 
"Mark" 
0.0 
"Alice" 
0.0 
We can see that Doug is the most popular user in our imaginary social network graph, with 5 followers  all other users follow them, but they don’t follow anybody back. In a real social network, celebrities have very high follower counts but tend to follow only very few people. We could therefore consider Doug quite the celebrity!
4.3. Stats
In the stats
execution mode, the algorithm returns a single row containing a summary of the algorithm result.
This execution mode does not have any side effects.
It can be useful for evaluating algorithm performance by inspecting the computeMillis
return item.
In the examples below we will omit returning the timings.
The full signature of the procedure can be found in the syntax section.
For more details on the stats
mode in general, see Stats.
stats
mode:CALL gds.degree.stats('myGraph')
YIELD centralityDistribution
RETURN centralityDistribution.min AS minimumScore, centralityDistribution.mean AS meanScore
minimumScore  meanScore 

0.0 
1.3333358764648438 
Comparing this to the results we saw in the stream example, we can find our minimum and mean values from the table.
4.4. Mutate
The mutate
execution mode extends the stats
mode with an important side effect: updating the named graph with a new node property containing the degree centrality for that node.
The name of the new property is specified using the mandatory configuration parameter mutateProperty
.
The result is a single summary row, similar to stats
, but with some additional metrics.
The mutate
mode is especially useful when multiple algorithms are used in conjunction.
For more details on the mutate
mode in general, see Mutate.
mutate
mode:CALL gds.degree.mutate('myGraph', { mutateProperty: 'degree' })
YIELD centralityDistribution, nodePropertiesWritten
RETURN centralityDistribution.min AS minimumScore, centralityDistribution.mean AS meanScore, nodePropertiesWritten
minimumScore  meanScore  nodePropertiesWritten 

0.0 
1.3333358764648438 
6 
The returned result is the same as in the stats
example.
Additionally, the graph 'myGraph' now has a node property degree
which stores the degree centrality score for each node.
To find out how to inspect the new schema of the inmemory graph, see Listing graphs in the catalog.
4.5. Write
The write
execution mode extends the stats
mode with an important side effect: writing the degree centrality for each node as a property to the Neo4j database.
The name of the new property is specified using the mandatory configuration parameter writeProperty
.
The result is a single summary row, similar to stats
, but with some additional metrics.
The write
mode enables directly persisting the results to the database.
For more details on the write
mode in general, see Write.
write
mode:CALL gds.degree.write('myGraph', { writeProperty: 'degree' })
YIELD centralityDistribution, nodePropertiesWritten
RETURN centralityDistribution.min AS minimumScore, centralityDistribution.mean AS meanScore, nodePropertiesWritten
minimumScore  meanScore  nodePropertiesWritten 

0.0 
1.3333358764648438 
6 
The returned result is the same as in the stats
example.
Additionally, each of the seven nodes now has a new property degree
in the Neo4j database, containing the degree centrality score for that node.
5. Weighted Degree Centrality example
This example will explain the weighted Degree Centrality algorithm. This algorithm is a variant of the Degree Centrality algorithm, that measures the sum of positive weights of incoming and outgoing relationships.
stream
mode, showing which users have the highest weighted degree centrality:CALL gds.degree.stream(
'myGraph',
{ relationshipWeightProperty: 'score' }
)
YIELD nodeId, score
RETURN gds.util.asNode(nodeId).name AS name, score AS weightedFollowers
ORDER BY weightedFollowers DESC, name DESC
name  weightedFollowers 

"Doug" 
7.5 
"Charles" 
5.0 
"Michael" 
4.5 
"Mark" 
0.0 
"Bridget" 
0.0 
"Alice" 
0.0 
Doug still remains our most popular user, but there isn’t such a big gap to the next person.
Charles and Michael both only have one follower, but those relationships have a high relationship weight.
Note that Bridget also has a weighted score of 0.0, despite having a connection from Alice.
That is because the score
property value between Bridget and Alice is negative and will be ignored by the algorithm.
6. Setting an orientation
By default, node centrality uses the NATURAL
orientation to compute degrees.
For some usecases it makes sense to analyze a different orientation, for example, if we want to find out how many users follow another user.
In order to change the orientation, we can use the orientation
configuration key.
There are three supported values:

NATURAL
(default) corresponds to computing the outdegree of each node. 
REVERSE
corresponds to computing the indegree of each node. 
UNDIRECTED
computes and sums both the outdegree and indegree of each node.
stream
mode, showing which users have the highest indegree centrality using the reverse orientation of the relationships:CALL gds.degree.stream(
'myGraph',
{ orientation: 'REVERSE' }
)
YIELD nodeId, score
RETURN gds.util.asNode(nodeId).name AS name, score AS followees
ORDER BY followees DESC, name DESC
name  followees 

"Alice" 
3.0 
"Mark" 
2.0 
"Michael" 
1.0 
"Charles" 
1.0 
"Bridget" 
1.0 
"Doug" 
0.0 
The example shows that when looking at the reverse orientation, Alice
is more central in the network than Doug
.
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