HITS

This section describes the HITS algorithm in the Neo4j Graph Data Science library.

1. Introduction

The Hyperlink-Induced Topic Search (HITS) is a link analysis algorithm that rates nodes based on two scores, a hub score and an authority score. The authority score estimates the importance of the node within the network. The hub score estimates the value of its relationships to other nodes. The GDS implementation is based on the Authoritative Sources in a Hyperlinked Environment publication by Jon M. Kleinberg.

2. Syntax

This section covers the syntax used to execute the HITS 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.

Example 1. HITS syntax per mode
Run HITS in stream mode on a named graph.
CALL gds.alpha.hits.stream(
  graphName: String,
  configuration: Map
)
YIELD
  nodeId: Integer,
  values: Map {
    hub: Float,
    auth: Float
  }
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. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

nodeLabels

String[]

['*']

yes

Filter the named graph using the given node labels.

relationshipTypes

String[]

['*']

yes

Filter the named graph using the given relationship types.

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm.

Table 3. Algorithm specific configuration
Name Type Default Optional Description

hitsIterations

Integer

n/a

no

The number of hits iterations to run. The number of pregel iterations will be equal to hitsIterations * 4 + 1

authProperty

String

"auth"

yes

The name that is used for the auth property when using STREAM, MUTATE or WRITE modes.

hubProperty

String

"hub"

yes

The name that is used for the hub property when using STREAM, MUTATE or WRITE modes.

Table 4. Results
Name Type Description

nodeId

Integer

Node ID.

values

Map

A map containing the auth and hub keys.

Run HITS in stats mode on a named graph.
CALL gds.alpha.hits.stats(
  graphName: String,
  configuration: Map
)
YIELD
  ranIterations: Integer,
  didConverge: Boolean,
  createMillis: Integer,
  computeMillis: Integer,
  configuration: Map
Table 5. 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 6. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

nodeLabels

String[]

['*']

yes

Filter the named graph using the given node labels.

relationshipTypes

String[]

['*']

yes

Filter the named graph using the given relationship types.

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm.

Table 7. Algorithm specific configuration
Name Type Default Optional Description

hitsIterations

Integer

n/a

no

The number of hits iterations to run. The number of pregel iterations will be equal to hitsIterations * 4 + 1

authProperty

String

"auth"

yes

The name that is used for the auth property when using STREAM, MUTATE or WRITE modes.

hubProperty

String

"hub"

yes

The name that is used for the hub property when using STREAM, MUTATE or WRITE modes.

Table 8. Results
Name Type Description

ranIterations

Integer

Number of iterations run.

didConverge

Boolean

Indicates if the algorithm converged.

createMillis

Integer

Milliseconds for creating the graph.

computeMillis

Integer

Milliseconds for running the algorithm.

configuration

Map

Configuration used for running the algorithm.

Run HITS in mutate mode on a named graph.
CALL gds.alpha.hits.mutate(
  graphName: String,
  configuration: Map
)
YIELD
  ranIterations: Integer,
  didConverge: Boolean,
  createMillis: Integer,
  computeMillis: Integer,
  mutateMillis: Integer,
  nodePropertiesWritten: Integer,
  configuration: Map
Table 9. 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 10. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

nodeLabels

String[]

['*']

yes

Filter the named graph using the given node labels.

relationshipTypes

String[]

['*']

yes

Filter the named graph using the given relationship types.

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm.

mutateProperty

String

""

yes

The prefix used for all public properties in the PregelSchema.

Table 11. Algorithm specific configuration
Name Type Default Optional Description

hitsIterations

Integer

n/a

no

The number of hits iterations to run. The number of pregel iterations will be equal to hitsIterations * 4 + 1

authProperty

String

"auth"

yes

The name that is used for the auth property when using STREAM, MUTATE or WRITE modes.

hubProperty

String

"hub"

yes

The name that is used for the hub property when using STREAM, MUTATE or WRITE modes.

Table 12. Results
Name Type Description

ranIterations

Integer

The number of iterations run.

didConverge

Boolean

Indicates if the algorithm converged.

createMillis

Integer

Milliseconds for creating the graph.

computeMillis

Integer

Milliseconds for running the algorithm.

mutateMillis

Integer

Milliseconds for adding properties to the in-memory graph.

nodePropertiesWritten

Integer

The number of properties that were written to Neo4j.

configuration

Map

The configuration used for running the algorithm.

Run HITS in write mode on a named graph.
CALL gds.alpha.hits.write(
  graphName: String,
  configuration: Map
)
YIELD
  ranIterations: Integer,
  didConverge: Boolean,
  createMillis: Integer,
  computeMillis: Integer,
  writeMillis: Integer,
  nodePropertiesWritten: Integer,
  configuration: Map
Table 13. 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 14. General configuration for algorithm execution on a named graph.
Name Type Default Optional Description

nodeLabels

String[]

['*']

yes

Filter the named graph using the given node labels.

relationshipTypes

String[]

['*']

yes

Filter the named graph using the given relationship types.

concurrency

Integer

4

yes

The number of concurrent threads used for running the algorithm. Also provides the default value for 'writeConcurrency'.

writeConcurrency

Integer

value of 'concurrency'

yes

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

writeProperty

String

""

yes

The prefix used for all public properties in the PregelSchema.

Table 15. Algorithm specific configuration
Name Type Default Optional Description

hitsIterations

Integer

n/a

no

The number of hits iterations to run. The number of pregel iterations will be equal to hitsIterations * 4 + 1

authProperty

String

"auth"

yes

The name that is used for the auth property when using STREAM, MUTATE or WRITE modes.

hubProperty

String

"hub"

yes

The name that is used for the hub property when using STREAM, MUTATE or WRITE modes.

Table 16. Results
Name Type Description

ranIterations

Integer

The number of iterations run.

didConverge

Boolean

Indicates if the algorithm converged.

createMillis

Integer

Milliseconds for creating the graph.

computeMillis

Integer

Milliseconds for running the algorithm.

writeMillis

Integer

Milliseconds for writing result data back.

nodePropertiesWritten

Integer

The number of properties that were written to Neo4j.

configuration

Map

The configuration used for running the algorithm.

3. Examples

In this section we will show examples of running the HITS 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:

Visualization of the example graph
The following Cypher statement will create the example graph in the Neo4j database:
CREATE
  (a:Website {name: 'A'}),
  (b:Website {name: 'B'}),
  (c:Website {name: 'C'}),
  (d:Website {name: 'D'}),
  (e:Website {name: 'E'}),
  (f:Website {name: 'F'}),
  (g:Website {name: 'G'}),
  (h:Website {name: 'H'}),
  (i:Website {name: 'I'}),

  (a)-[:LINK]->(b),
  (a)-[:LINK]->(c),
  (a)-[:LINK]->(d),
  (b)-[:LINK]->(c),
  (b)-[:LINK]->(d),
  (c)-[:LINK]->(d),

  (e)-[:LINK]->(b),
  (e)-[:LINK]->(d),
  (e)-[:LINK]->(f),
  (e)-[:LINK]->(h),

  (f)-[:LINK]->(g),
  (f)-[:LINK]->(i),
  (f)-[:LINK]->(h),
  (g)-[:LINK]->(h),
  (g)-[:LINK]->(i),
  (h)-[:LINK]->(i);

In the example, we will use the HITS algorithm to calculate the authority and hub scores.

The following statement will create the graph and store it in the graph catalog.
CALL gds.graph.create(
  'myGraph',
  'Website',
  'LINK'
);

In the following examples we will demonstrate using the HITS algorithm on this graph.

3.1. Stream

In the stream execution mode, the algorithm returns the authority and hub scores for each node. 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, and stream results:
CALL gds.alpha.hits.stream('myGraph', {hitsIterations: 20})
YIELD nodeId, values
RETURN gds.util.asNode(nodeId).name AS Name, values.auth AS auth, values.hub as hub
ORDER BY Name ASC
Table 17. Results
Name auth hub

"A"

0.0

0.5147630377521207

"B"

0.42644630743935796

0.3573686670593437

"C"

0.3218729455718005

0.23857061715828276

"D"

0.6463862608483191

0.0

"E"

0.0

0.640681017095129

"F"

0.23646490227616518

0.2763222153580397

"G"

0.10200264424057169

0.23867470447760597

"H"

0.426571816146601

0.0812340105698113

"I"

0.22009646020698218

0.0