Article Rank

Introduction

ArticleRank is a variant of the Page Rank algorithm, which measures the transitive influence of nodes.

Page Rank follows the assumption that relationships originating from low-degree nodes have a higher influence than relationships from high-degree nodes. Article Rank lowers the influence of low-degree nodes by lowering the scores being sent to their neighbors in each iteration.

The Article Rank of a node v at iteration i is defined as:

articleRank

where,

  • Nin(v) denotes incoming neighbors and Nout(v) denotes outgoing neighbors of node v.

  • d is a damping factor in [0, 1].

  • Nout is the average out-degree

For more information, see ArticleRank: a PageRank‐based alternative to numbers of citations for analysing citation networks.

Considerations

There are some things to be aware of when using the Article Rank 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 Article Rank algorithm.

Run ArticleRank.
CALL graph.article_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 Article 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

resultProperty

String

'articleRank'

yes

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

dampingFactor

Float

0.85

yes

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

maxIterations

Integer

20

yes

The maximum number of iterations of Article 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 Article Rank. To use different bias for different source nodes, use the syntax: [[nodeId1, bias1], [nodeId2, bias2], …​].

sourceNodesTable

String

null

yes1

The name of the table containing the source nodes.

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', …​}.

1 The sourceNodesTable parameter is mandatory when the sourceNodes parameter is specified.

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

'articleRank'

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 Article Rank 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 of 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 VARCHAR);
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 VARCHAR, TARGETNODEID VARCHAR, WEIGHT FLOAT);
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 Article Rank 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 Article Rank job:
CALL Neo4j_Graph_Analytics.graph.article_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'resultProperty': 'centrality'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'centrality'
    }]
});
Table 5. Results
JOB_ID JOB_STATUS JOB_START JOB_END JOB_RESULT

job_24fed6a63ca84794babf21b606333bd6

SUCCESS

2026-02-16 09:16:17.294

2026-02-16 09:16:24.413

 
 {
    "article_rank_1": {
      "centralityDistribution": {
        "max": 0.5607109069824218,
        "mean": 0.2547265291213989,
        "min": 0.18152332305908203,
        "p50": 0.18152332305908203,
        "p75": 0.2503366470336914,
        "p90": 0.5607099533081055,
        "p95": 0.5607099533081055,
        "p99": 0.5607099533081055,
        "p999": 0.5607099533081055
      },
      "computeMillis": 220,
      "configuration": {
        "concurrency": 2,
        "dampingFactor": 0.85,
        "maxIterations": 20,
        "nodeLabels": ["*"],
        "relationshipTypes": ["*"],
        "resultProperty": "articleRank",
        "scaler": "NONE",
        "sourceNodes": [],
        "tolerance": 1.000000000000000e-07
      },
      "didConverge": true,
      "ranIterations": 19
    },
    "project_graph_1": {
      "graphName": "snowgraph",
      "nodeCount": 8,
      "nodeLabels": ...,
      "nodeMillis": 394,
      "relationshipCount": 14,
      "relationshipMillis": 629,
      "relationshipTypes": ...,
      "totalMillis": 1023
    },
    "write_node_property_1": {
      "copyIntoTableMillis": 955,
      "nodeLabel": "PAGES",
      "nodeProperty": "articleRank",
      "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
      "rowsWritten": 8,
      "stageUploadMillis": 1552,
      "writeMillis": 2721
    }
}

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 eight 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 centrality DESC;
Table 6. Results
NODEID CENTRALITY

Home

0.5607071761939444

About

0.250337073634706

Links

0.250337073634706

Product

0.250337073634706

Site A

0.18152391630760797

Site B

0.18152391630760797

Site C

0.18152391630760797

Site D

0.18152391630760797

The above query is running the Article Rank 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 considers the relationships of the graph to be unweighted. To change this behaviour, we can use the relationshipWeightProperty configuration parameter. If the parameter is set, the associated property value is used as relationship weight. In the weighted case, the previous score of a node sent to its neighbors is multiplied by the normalized relationship weight. Note, that negative relationship weights are ignored during the computation.

In the following example, we use the weight property of the input graph as relationship weight property.

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

job_acdcd121d84c49bdb50739ce7c1fe07f

SUCCESS

2025-06-25 09:54:25.390

2025-06-25 09:54:30.822

 
 {
  "article_rank_1": {
    "centralityDistribution": {
      "max": 0.5160827636718749,
      "mean": 0.21710503101348877,
      "min": 0.15281105041503906,
      "p50": 0.15281105041503906,
      "p75": 0.18190288543701172,
      "p90": 0.5160818099975586,
      "p95": 0.5160818099975586,
      "p99": 0.5160818099975586,
      "p999": 0.5160818099975586
    },
    "computeMillis": 211,
    "configuration": {
      "concurrency": 2,
      "dampingFactor": 0.85,
      "maxIterations": 20,
      "nodeLabels": ["*"],
      "relationshipTypes": ["*"],
      "relationshipWeightProperty": "WEIGHT",
      "resultProperty": "centrality",
      "scaler": "NONE",
      "sourceNodes": [],
      "tolerance": 1.000000000000000e-07
    },
    "didConverge": true,
    "ranIterations": 14
  },
  "project_graph_1": {
    "graphName": "snowgraph",
    "nodeCount": 8,
    "nodeLabels": ...,
    "nodeMillis": 866,
    "relationshipCount": 14,
    "relationshipMillis": 874,
    "relationshipTypes": ...,
    "totalMillis": 1740
  },
  "write_node_property_1": {
    "copyIntoTableMillis": 1656,
    "nodeLabel": "PAGES",
    "nodeProperty": "centrality",
    "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
    "rowsWritten": 8,
    "stageUploadMillis": 1626,
    "writeMillis": 3606
  }
}
 
SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY centrality DESC;
Table 8. Results
NODEID CENTRALITY

Home

0.5160810726222141

Product

0.24570958074084706

About

0.1819031935802824

Links

0.1819031935802824

Site A

0.15281123078335393

Site B

0.15281123078335393

Site C

0.15281123078335393

Site D

0.15281123078335393

As in the unweighted example, the "Home" node has the highest score. In contrast, the "Product" now has the second highest instead of the fourth-highest score.

=== Tolerance

The tolerance configuration parameter denotes the minimum change in scores between iterations. If all scores change less than the configured tolerance, the iteration is aborted and considered converged. Note, that setting a higher tolerance leads to earlier convergence, but also to less accurate centrality scores.

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

job_c9869bd231a943a3961b830677b9acc6

SUCCESS

2025-06-25 09:59:32.257

2025-06-25 09:59:37.375

 
 {
  "article_rank_1": {
    "centralityDistribution": {
      "max": 0.44707107543945307,
      "mean": 0.22657835483551025,
      "min": 0.16888809204101562,
      "p50": 0.16888809204101562,
      "p75": 0.23000144958496094,
      "p90": 0.4470701217651367,
      "p95": 0.4470701217651367,
      "p99": 0.4470701217651367,
      "p999": 0.4470701217651367
    },
    "computeMillis": 139,
    "configuration": {
      "concurrency": 2,
      "dampingFactor": 0.85,
      "maxIterations": 20,
      "nodeLabels": ["*"],
      "relationshipTypes": ["*"],
      "resultProperty": "centrality",
      "scaler": "NONE",
      "sourceNodes": [],
      "tolerance": 0.1
    },
    "didConverge": true,
    "ranIterations": 2
  },
  "project_graph_1": {
    "graphName": "snowgraph",
    "nodeCount": 8,
    "nodeLabels": ...,
    "nodeMillis": 430,
    "relationshipCount": 14,
    "relationshipMillis": 715,
    "relationshipTypes": ...,
    "totalMillis": 1145
  },
  "write_node_property_1": {
    "copyIntoTableMillis": 969,
    "nodeLabel": "PAGES",
    "nodeProperty": "centrality",
    "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
    "rowsWritten": 8,
    "stageUploadMillis": 1532,
    "writeMillis": 2735
  }
}
 
SELECT * FROM EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY ORDER BY centrality DESC;
Table 10. Results
NODEID CENTRALITY

Home

0.4470707071

About

0.2300021265

Links

0.2300021265

Product

0.2300021265

Site A

0.1688888889

Site B

0.1688888889

Site C

0.1688888889

Site D

0.1688888889

We are using tolerance: 0.1, which leads to slightly different results compared to the example. However, the computation converges after two iterations, and we can already observe a trend in the resulting scores.

=== Personalized Article Rank

Personalized Article Rank is a variation of Article Rank which is biased towards a set of sourceNodes. By default, the random walk teleports to any node in the graph with equal probability. Like in PageRank, this can be changed to only a set of sourceNodes instead.

The following examples show how to run Article Rank centered around 'Site A' and 'Site B'.

The following will run the algorithm and stream results:
CALL Neo4j_Graph_Analytics.graph.article_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'resultProperty': 'centrality',
        'maxIterations': 20,
        'dampingFactor': 0.85,
        'sourceNodes': ['Site A'],
        'sourceNodesTable': 'PAGES'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'centrality'
    }]
});
Table 11. Results
JOB_ID JOB_STATUS JOB_START JOB_END JOB_RESULT

job_cb7c798e6fa64230acb25baf69ba245c

SUCCESS

2025-06-25 10:08:14.987

2025-06-25 10:08:19.910

 
 {
  "article_rank_1": {
    "centralityDistribution": {
      "max": 0.15124607086181638,
      "mean": 0.029988674446940422,
      "min": 0.001245245337486267,
      "p50": 0.009888879954814911,
      "p75": 0.009888879954814911,
      "p90": 0.1512460634112358,
      "p95": 0.1512460634112358,
      "p99": 0.1512460634112358,
      "p999": 0.1512460634112358
    },
    "computeMillis": 141,
    "configuration": {
      "concurrency": 2,
      "dampingFactor": 0.85,
      "maxIterations": 20,
      "nodeLabels": ["*"],
      "relationshipTypes": ["*"],
      "resultProperty": "centrality",
      "scaler": "NONE",
      "sourceNodes": [
        "Site A"
      ],
      "sourceNodesTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES",
      "tolerance": 1.000000000000000e-07
    },
    "didConverge": true,
    "ranIterations": 16
  },
  "project_graph_1": {
    "graphName": "snowgraph",
    "nodeCount": 8,
    "nodeLabels": ...,
    "nodeMillis": 397,
    "relationshipCount": 14,
    "relationshipMillis": 742,
    "relationshipTypes": ...,
    "totalMillis": 1139
  },
  "write_node_property_1": {
    "copyIntoTableMillis": 1074,
    "nodeLabel": "PAGES",
    "nodeProperty": "centrality",
    "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
    "rowsWritten": 8,
    "stageUploadMillis": 1431,
    "writeMillis": 2724
  }
}

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 centrality DESC;
Table 12. Results
NODEID CENTRALITY

Site A

0.15124525255992738

Home

0.055261428833430645

About

0.009888887264929692

Product

0.009888887264929692

Links

0.009888887264929692

Site B

0.001245252559927339

Site C

0.001245252559927339

Site D

0.001245252559927339

Biased Personalized Article Rank

Similarly to Personalized Article Rank, the algorithm allows weighing the sourceNodes differently, increasing the likeliness of teleportation to some nodes more than others.

The following example shows how to run Article Rank 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 the algorithm and stream results:
CALL Neo4j_Graph_Analytics.graph.article_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'resultProperty': 'centrality',
        'maxIterations': 20,
        'dampingFactor': 0.85,
        'sourceNodes': [['Site A', 1], ['Site B', 2]],
        'sourceNodesTable': 'PAGES'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'centrality'
    }]
});
Table 13. Results
JOB_ID JOB_STATUS JOB_START JOB_END JOB_RESULT

job_9f6c8cc7b49f46caa922743d671d0081

SUCCESS

2025-06-25 10:14:10.288

2025-06-25 10:14:15.641

 
 {
  "article_rank_1": {
    "centralityDistribution": {
      "max": 0.3037376403808593,
      "mean": 0.0899660550057888,
      "min": 0.0037357956171035767,
      "p50": 0.02966676652431488,
      "p75": 0.15373609960079193,
      "p90": 0.3037376254796982,
      "p95": 0.3037376254796982,
      "p99": 0.3037376254796982,
      "p999": 0.3037376254796982
    },
    "computeMillis": 145,
    "configuration": {
      "concurrency": 2,
      "dampingFactor": 0.85,
      "maxIterations": 20,
      "nodeLabels": ["*"],
      "relationshipTypes": ["*"],
      "resultProperty": "centrality",
      "scaler": "NONE",
      "sourceNodes": [["Site A", 1], ["Site B", 2]],
      "sourceNodesTable": "EXAMPLE_DB.PUBLIC.PAGES",
      "tolerance": 1.000000000000000e-07
    },
    "didConverge": true,
    "ranIterations": 17
  },
  "project_graph_1": {
    "graphName": "snowgraph",
    "nodeCount": 8,
    "nodeLabels": ...,
    "nodeMillis": 435,
    "relationshipCount": 14,
    "relationshipMillis": 747,
    "relationshipTypes": ...,
    "totalMillis": 1182
  },
  "write_node_property_1": {
    "copyIntoTableMillis": 1352,
    "nodeLabel": "PAGES",
    "nodeProperty": "centrality",
    "outputTable": "EXAMPLE_DB.PUBLIC.PAGES_CENTRALITY",
    "rowsWritten": 8,
    "stageUploadMillis": 1398,
    "writeMillis": 3021
  }
}

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 centrality DESC;
Table 14. Results
NODEID CENTRALITY

Site B

0.3037358066855114

Home

0.16578479041558442

Site A

0.15373580668551137

About

0.029666736048867288

Product

0.029666736048867288

Links

0.029666736048867288

Site C

0.003735806685511373

Site D

0.003735806685511373

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 Article Rank job with a scaler:
CALL Neo4j_Graph_Analytics.graph.article_rank('CPU_X64_XS', {
    'defaultTablePrefix': 'EXAMPLE_DB.DATA_SCHEMA',
    'project': {
        'nodeTables': [ 'PAGES' ],
        'relationshipTables': {
            'LINKS': {
                'sourceTable': 'PAGES',
                'targetTable': 'PAGES'
            }
        }
    },
    'compute': {
        'resultProperty': 'centrality',
        'scaler': 'StdScore'
    },
    'write': [{
        'nodeLabel': 'PAGES',
        'outputTable': 'PAGES_CENTRALITY',
        'nodeProperty': 'centrality'
    }]
});
Table 15. Results
JOB_ID JOB_STATUS JOB_START JOB_END JOB_RESULT

job_69fe344cccb44ef7adde9ed5868f2166

SUCCESS

2025-06-24 13:47:43.484

2025-06-24 13:47:48.661

 
 {
  "article_rank_1": {
    "centralityDistribution": {
      "Error": "Unable to create histogram due to range of scores exceeding implementation limits."
    },
    "computeMillis": 108,
    "configuration": {
      "concurrency": 2,
      "dampingFactor": 0.85,
      "maxIterations": 20,
      "nodeLabels": ["*"],
      "relationshipTypes": ["*"],
      "resultProperty": "centrality",
      "scaler": "STDSCORE",
      "sourceNodes": [],
      "tolerance": 1.000000000000000e-07
    },
    "didConverge": true,
    "ranIterations": 19
  },
  "project_graph_1": {
    "graphName": "snowgraph",
    "nodeCount": 8,
    "nodeLabels": ...,
    "nodeMillis": 272,
    "relationshipCount": 14,
    "relationshipMillis": 793,
    "relationshipTypes": ...,
    "totalMillis": 1065
  },
  "write_node_property_1": {
    "copyIntoTableMillis": 1260,
    "nodeLabel": "PAGES",
    "nodeProperty": "centrality",
    "outputTable": "EXAMPLE_DB.DATA_SCHEMA.PAGES_CENTRALITY",
    "rowsWritten": 8,
    "stageUploadMillis": 1739,
    "writeMillis": 3353
  }
}

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 centrality DESC;
Table 16. Results
NODEID CENTRALITY

Home

2.550761988515413

About

-0.036593974039467986

Product

-0.036593974039467986

Links

-0.036593974039467986

Site A

-0.6102450165992518

Site B

-0.6102450165992518

Site C

-0.6102450165992518

Site D

-0.6102450165992518

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.