PageRank

Introduction

The PageRank algorithm measures the importance of each node within the graph, based on the number of incoming relationships and the importance of the corresponding source nodes. The underlying assumption, roughly speaking, is that a page is only as important as the pages that link to it.

PageRank is introduced in the original Google paper as a function that solves the following equation:

page rank formula

where,

  • we assume that a page A has pages T1 to Tn which point to it.

  • d is a damping factor which can be set between 0 (inclusive) and 1 (exclusive). It is usually set to 0.85.

  • C(A) is defined as the number of links going out of page A.

This equation is used to iteratively update a candidate solution and arrive at an approximate solution to the same equation.

For more information on this algorithm, see:

Considerations

There are some things to be aware of when using the PageRank algorithm:

  • If there are no relationships from within a group of pages to outside the group, then the group is considered a spider trap.

  • Rank sink can occur when a network of pages is forming an infinite cycle.

  • Dead-ends occur when pages have no outgoing relationship.

Changing the damping factor can help with all the considerations above. It can be interpreted as a probability of a web surfer to sometimes jump to a random page and therefore not getting stuck in sinks.

Syntax

This section covers the syntax used to execute the PageRank algorithm.

Run PageRank.
CALL graph.page_rank(
  'CPU_X64_XS',                    (1)
  {
    ['defaultTablePrefix': '...',] (2)
    'project': {...},              (3)
    'compute': {...},              (4)
    'write':   {...}               (5)
  }
);
1 Compute pool selector.
2 Optional prefix for table references.
3 Project config.
4 Compute config.
5 Write config.
Table 1. Parameters
Name Type Default Optional Description

computePoolSelector

String

n/a

no

The selector for the compute pool on which to run the Page Rank job.

configuration

Map

{}

no

Configuration for graph project, algorithm compute and result write back.

The configuration map consists of the following three entries.

For more details on below Project configuration, refer to the Project documentation.
Table 2. Project configuration
Name Type

nodeTables

List of node tables.

relationshipTables

Map of relationship types to relationship tables.
Table 3. Compute configuration
Name Type Default Optional Description

mutateProperty

String

'pageRank'

yes

The node property that will be written back to the Snowflake database.

dampingFactor

Float

0.85

yes

The damping factor of the Page Rank calculation. Must be in [0, 1).

maxIterations

Integer

20

yes

The maximum number of iterations of Page Rank to run.

tolerance

Float

0.0000001

yes

Minimum change in scores between iterations. If all scores change less than the tolerance value the result is considered stable and the algorithm returns.

relationshipWeightProperty

String

null

yes

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

sourceNodes

Node/Number or List or List of pairs as lists

[]

yes

The nodes or node ids or node-bias pairs to use for computing Personalized Page Rank. To use different bias for different source nodes, use the use the syntax: [[nodeId1, bias1], [nodeId2, bias2], …​].

scaler

String or Map

None

yes

The name of the scaler applied for the final scores. Supported values are None, MinMax, Max, Mean, Log, and StdScore. To apply scaler-specific configuration, use the Map syntax: {scaler: 'name', …​}.
For more details on below Write configuration, refer to the Write documentation.
Table 4. Write configuration
Name Type Default Optional Description

nodeLabel

String

n/a

no

Node label in the in-memory graph from which to write a node property.

nodeProperty

String

'pageRank'

yes

The node property that will be written back to the Snowflake database.

outputTable

String

n/a

no

Table in Snowflake database to which node properties are written.

Examples

In this section we will show examples of running the PageRank 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 web network graph of a handful nodes connected in a particular pattern. The example graph looks like this:

Visualization of the example graph
The following SQL statement will create the example graph tables in the Snowflake database:
CREATE OR REPLACE TABLE EXAMPLE_DB.DATA_SCHEMA.PAGES (NODEID STRING);
INSERT INTO EXAMPLE_DB.DATA_SCHEMA.PAGES VALUES
  ('Home'),
  ('About'),
  ('Product'),
  ('Links'),
  ('Site A'),
  ('Site B'),
  ('Site C'),
  ('Site D');

CREATE OR REPLACE TABLE EXAMPLE_DB.DATA_SCHEMA.LINKS (SOURCENODEID STRING, TARGETNODEID STRING, WEIGHT DOUBLE);
INSERT INTO EXAMPLE_DB.DATA_SCHEMA.LINKS VALUES
  ('Home',    'About',   0.2),
  ('Home',    'Links',   0.2),
  ('Home',    'Product', 0.6),
  ('About',   'Home',    1.0),
  ('Product', 'Home',    1.0),
  ('Site A',  'Home',    1.0),
  ('Site B',  'Home',    1.0),
  ('Site C',  'Home',    1.0),
  ('Site D',  'Home',    1.0),
  ('Links',   'Home',    0.8),
  ('Links',   'Site A',  0.05),
  ('Links',   'Site B',  0.05),
  ('Links',   'Site C',  0.05),
  ('Links',   'Site D',  0.05);

This graph represents eight pages, linking to one another. Each relationship has a property called weight, which describes the importance of the relationship.

Run job

Running a PageRank job involves the three steps: Project, Compute and Write.

To run the query, there is a required setup of grants for the application, your consumer role and your environment. Please see the Getting started page for more on this.

We also assume that the application name is the default Neo4j_Graph_Analytics. If you chose a different app name during installation, please replace it with that.

The following will run a PageRank job:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 5. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_389ecfb0408e407187049486effebf43

2025-06-25 09:48:14.968

2025-06-25 09:48:20.425

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "max": 3.215682983398437,
        "mean": 0.9612393379211426,
        "min": 0.32785606384277344,
        "p50": 0.32785606384277344,
        "p75": 1.0542736053466797,
        "p90": 3.2156810760498047,
        "p95": 3.2156810760498047,
        "p99": 3.2156810760498047,
        "p999": 3.2156810760498047
      },
      "computeMillis": 106,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "jobId": "11d69048-32b1-49f0-8b93-574a54d55b71",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "scaler": "NONE",
        "sourceNodes": [],
        "sudo": false,
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": false,
      "mutateMillis": 3,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 53,
      "preProcessingMillis": 9,
      "ranIterations": 20
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 291,
      "relationshipCount": 14,
      "relationshipMillis": 442,
      "totalMillis": 733
    },
    "write_node_property_1": {
      "exportMillis": 2100,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}

The returned result contains information about the job execution and result distribution. The centrality distribution histogram can be useful for inspecting the computed scores or perform normalizations. Additionally, the centrality score for each of the seven nodes has been written back to the Snowflake database. We can query it like so:

SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 6. Results
NODEID SCORE

Home

3.215682

About

1.054270055

Product

1.054270055

Links

1.054270055

Site A

0.3278578964

Site B

0.3278578964

Site C

0.3278578964

Site D

0.3278578964

The above query is running the PageRank algorithm mode as unweighted and the returned scores are not normalized. Below, one can find an example for weighted graphs. Another example shows the application of a scaler to normalize the final scores.

Weighted

By default, the algorithm is considering the relationships of the graph to be unweighted, to change this behaviour we can use configuration parameter called relationshipWeightProperty. In the weighted case, the previous score of a node send to its neighbours, is multiplied by the relationship weight and then divided by the sum of the weights of its outgoing relationships. If the value of the relationship property is negative, it will be ignored during computation. Below is an example of running the algorithm using the relationship property.

The following will run a PageRank job with weights:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score',
        'maxIterations': 20,
        'dampingFactor': 0.85,
        'relationshipWeightProperty': 'WEIGHT'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 7. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_acdcd121d84c49bdb50739ce7c1fe07f

2025-06-25 09:54:25.390

2025-06-25 09:54:30.822

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "max": 3.537521362304687,
        "mean": 0.9612407684326172,
        "min": 0.18152618408203125,
        "p50": 0.18152618408203125,
        "p75": 0.7452611923217773,
        "p90": 3.537520408630371,
        "p95": 3.537520408630371,
        "p99": 3.537520408630371,
        "p999": 3.537520408630371
      },
      "computeMillis": 101,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "jobId": "65745cab-4ed1-4477-b2cb-4997e66ea97e",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "relationshipWeightProperty": "WEIGHT",
        "scaler": "NONE",
        "sourceNodes": [],
        "sudo": false,
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": false,
      "mutateMillis": 2,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 58,
      "preProcessingMillis": 10,
      "ranIterations": 20
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 139,
      "relationshipCount": 14,
      "relationshipMillis": 593,
      "totalMillis": 732
    },
    "write_node_property_1": {
      "exportMillis": 1824,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}

Compared to the unweighted example, we see that Product has gained ranking, as expected:

SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 8. Results
NODEID SCORE

Home

3.537510284

Product

1.935783829

About

0.7452612764

Links

0.7452612764

Site A

0.1815267714

Site B

0.1815267714

Site C

0.1815267714

Site D

0.1815267714

Tolerance

The tolerance configuration parameter denotes the minimum change in scores between iterations. If all scores change less than the configured tolerance value the result stabilises, and the algorithm returns.

The following will run a PageRank job with tolerance:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score',
        'maxIterations': 20,
        'dampingFactor': 0.85,
        'tolerance': 0.1
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 9. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_3c7ea7a540594934b06adef0b1e8a55a

2025-06-25 09:59:32.257

2025-06-25 09:59:37.375

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "max": 1.581245422363281,
        "mean": 0.5387876033782959,
        "min": 0.2337493896484375,
        "p50": 0.2337493896484375,
        "p75": 0.5980215072631836,
        "p90": 1.5812444686889648,
        "p95": 1.5812444686889648,
        "p99": 1.5812444686889648,
        "p999": 1.5812444686889648
      },
      "computeMillis": 69,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "jobId": "b1013874-2865-4561-bf05-b7ebcba371e3",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "scaler": "NONE",
        "sourceNodes": [],
        "sudo": false,
        "tolerance": 0.1
      },
      "didConverge": true,
      "mutateMillis": 5,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 78,
      "preProcessingMillis": 15,
      "ranIterations": 6
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 151,
      "relationshipCount": 14,
      "relationshipMillis": 398,
      "totalMillis": 549
    },
    "write_node_property_1": {
      "exportMillis": 1810,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}
 
SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 10. Results
NODEID SCORE

Home

1.581245067

About

0.5980194356

Product

0.5980194356

Links

0.5980194356

Site A

0.2337495515

Site B

0.2337495515

Site C

0.2337495515

Site D

0.2337495515

Comparing to the original example, we get comparable results in a third of the time—six iterations instead of 20.

Damping Factor

The damping factor configuration parameter accepts values between zero (inclusive) and 1 (exclusive). If its value is too high, then problems of sinks and spider traps may occur, and the values may oscillate so that the algorithm does not converge. If it’s too low, then all scores are pushed towards 1, and the result will not sufficiently reflect the structure of the graph.

The following will run a PageRank job with tolerance:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score',
        'maxIterations': 20,
        'dampingFactor': 0.05
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 11. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_199788cefb85415aa435e07b4f0b16a7

2025-06-25 10:03:45.996

2025-06-25 10:03:51.061

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "max": 1.2487335205078123,
        "mean": 0.999997615814209,
        "min": 0.9597053527832031,
        "p50": 0.9597053527832031,
        "p75": 0.9708099365234375,
        "p90": 1.2487297058105469,
        "p95": 1.2487297058105469,
        "p99": 1.2487297058105469,
        "p999": 1.2487297058105469
      },
      "computeMillis": 76,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.05,
        "jobId": "9071a105-5dde-46ce-898e-f520b394f6c0",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "scaler": "NONE",
        "sourceNodes": [],
        "sudo": false,
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": true,
      "mutateMillis": 2,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 24,
      "preProcessingMillis": 20,
      "ranIterations": 6
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 188,
      "relationshipCount": 14,
      "relationshipMillis": 369,
      "totalMillis": 557
    },
    "write_node_property_1": {
      "exportMillis": 1934,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}
 
SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 12. Results
NODEID SCORE

Home

1.248730943

About

0.9708121819

Product

0.9708121819

Links

0.9708121819

Site A

0.9597081216

Site B

0.9597081216

Site C

0.9597081216

Site D

0.9597081216

Compared to the results from the original example which is using the default value of dampingFactor, the score values are closer to each other when using dampingFactor: 0.05. Quicker convergence (six iterations) at the expense of information.

Personalised PageRank

Personalized PageRank is a variation of PageRank which is biased towards a set of sourceNodes. This variant of PageRank is often used as part of recommender systems.

The following examples show how to run PageRank centered around 'Site A'.

The following will run a PageRank job with source nodes specified:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score',
        'maxIterations': 20,
        'dampingFactor': 0.85,
        'sourceNodes': ['Site A'],
        'sourceNodesTable': 'PAGES'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 13. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_83844b41641b48a8a2c547c14c4ff6d9

2025-06-25 10:08:14.987

2025-06-25 10:08:19.910

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "max": 0.3990230560302734,
        "mean": 0.12015484273433685,
        "min": 0.018903136253356934,
        "p50": 0.11220157146453857,
        "p75": 0.11220157146453857,
        "p90": 0.3990229368209839,
        "p95": 0.3990229368209839,
        "p99": 0.3990229368209839,
        "p999": 0.3990229368209839
      },
      "computeMillis": 77,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "jobId": "3767d8d4-1087-4981-9d33-c16bdb0d8746",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "scaler": "NONE",
        "sourceNodes": ["Site A"],
        "sourceNodesTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES",
        "sudo": false,
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": false,
      "mutateMillis": 4,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 68,
      "preProcessingMillis": 9,
      "ranIterations": 20
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 135,
      "relationshipCount": 14,
      "relationshipMillis": 355,
      "totalMillis": 490
    },
    "write_node_property_1": {
      "exportMillis": 1714,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}

We can see that by setting the focus on Site A, it moves up in the rankings:

SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 14. Results
NODEID SCORE

Home

0.3990229044

Site A

0.168903253

About

0.1122015175

Product

0.1122015175

Links

0.1122015175

Site B

0.01890325302

Site C

0.01890325302

Site D

0.01890325302

Biased Personalised PageRank

In GDS, personalized PageRank can also be run with a varying bias among the source nodes. Like regular personalized PageRank, this models a random walk that restarts at a specific set of source nodes. In the biased case, the likeliness of a restart (1-dampingFactor) stays the same but the destination of the restart will be biased according to settings.

The following example shows how to run PageRank centered around 'Site A' and 'Site B', with twice as high bias for 'Site B' than 'Site A'. The biased source nodes are entered as a list of node-value pairs (lists).

The following will run a PageRank job with source nodes specified:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score',
        'maxIterations': 20,
        'dampingFactor': 0.85,
        'sourceNodes': [['Site A', 1], ['Site B', 2]],
        'sourceNodesTable': 'PAGES'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 15. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_4c4c590a9dcb4df08a55d6e6e6f5e4c7

2025-06-25 10:14:10.288

2025-06-25 10:14:15.641

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "max": 1.1970748901367185,
        "mean": 0.3604651689529419,
        "min": 0.05670952796936035,
        "p50": 0.3366048336029053,
        "p75": 0.3366048336029053,
        "p90": 1.1970746517181396,
        "p95": 1.1970746517181396,
        "p99": 1.1970746517181396,
        "p999": 1.1970746517181396
      },
      "computeMillis": 66,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "jobId": "09044aff-b2be-4a14-84ce-ce8f36a394a8",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "scaler": "NONE",
        "sourceNodes": [["Site A",1],["Site B",2]],
        "sourceNodesTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES",
        "sudo": false,
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": false,
      "mutateMillis": 3,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 131,
      "preProcessingMillis": 14,
      "ranIterations": 20
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 138,
      "relationshipCount": 14,
      "relationshipMillis": 323,
      "totalMillis": 461
    },
    "write_node_property_1": {
      "exportMillis": 2104,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}

We observe that, since B receives the bias, B is ranked much more highly than A, which in turn is ranked more highly than C and D:

SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 16. Results
NODEID SCORE

Home

1.197068713

Site B

0.3567097591

About

0.3366045524

Product

0.3366045524

Links

0.3366045524

Site A

0.2067097591

Site C

0.05670975905

Site D

0.05670975905

Scaling centrality scores

To normalize the final scores as part of the algorithm execution, one can use the scaler configuration parameter. A description of all available scalers can be found in appendix: scalers.

Let’s look at it:

The following will run a PageRank job with a scaler:
CALL Neo4j_Graph_Analytics.graph.page_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'mutateProperty': 'score',
        'scaler': 'Mean'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'score'
    }]
});
Table 17. Results
JOB_ID JOB_START JOB_END JOB_RESULT

job_840d6ac0dfa245bb82456017a24d2b71

2025-06-24 13:47:43.484

2025-06-24 13:47:48.661

 
 {
    "page_rank_1": {
      "centralityDistribution": {
        "Error": "Unable to create histogram due to range of scores exceeding implementation limits."
      },
      "computeMillis": 136,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "jobId": "cdcb6b52-ab33-438b-8511-a3ac9a9fbe3a",
        "logProgress": true,
        "maxIterations": 20,
        "mutateProperty": "score",
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "scaler": "MEAN",
        "sourceNodes": [],
        "sudo": false,
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": false,
      "mutateMillis": 2,
      "nodePropertiesWritten": 8,
      "postProcessingMillis": 23,
      "preProcessingMillis": 7,
      "ranIterations": 20
    },
    "project_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeMillis": 195,
      "relationshipCount": 14,
      "relationshipMillis": 399,
      "totalMillis": 594
    },
    "write_node_property_1": {
      "exportMillis": 1891,
      "nodeLabel": "PAGES",
      "nodeProperty": "score",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "propertiesExported": 8
    }
}

As you can see in the output above, there are known limitations to recording probability distributions. It does not affect results.

SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY score DESC;
Table 18. Results
NODEID SCORE

Home

0.7806713464

About

0.03221442268

Product

0.03221442268

Links

0.03221442268

Site A

-0.2193286536

Site B

-0.2193286536

Site C

-0.2193286536

Site D

-0.2193286536

Comparing the results with the first example, we can see that the relative order of scores is the same, even if values have been scaled.