Centrality

algo.pagerank

Property Value

Procedure

algo.pagerank

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

1

Syntax

CALL algo.pagerank([{dampingFactor: 0.85, maxIterations: 20, tolerance: 0.0001, weightProperty: null}])
YIELD node, score

Parameters

Parameter Type Required Default Description

config map

Map

No

see defaults

Configuration properties (all optional)

dampingFactor

Double

No

0.85

Probability of following an edge vs. teleporting

maxIterations

Integer

No

20

Maximum number of power-iteration steps

tolerance

Double

No

0.0001

Convergence threshold (max score change)

weightProperty

String

No

null

Edge property for weighted PageRank

Yield Fields

Field Type Description

node

RID

Vertex identity

score

Double

PageRank score

Description

Computes the PageRank centrality score for every vertex using the power-iteration method. Dangling nodes (no outgoing edges) contribute their rank to all nodes proportionally via the teleportation mechanism. When weightProperty is specified, edge weights are used as transition probabilities (normalized per node).

Use Cases

  • Web page and document importance ranking

  • Identifying authoritative nodes in citation networks

  • Social network influence scoring

Example

CALL algo.pagerank({dampingFactor: 0.85, maxIterations: 30})
YIELD node, score
RETURN node, score ORDER BY score DESC LIMIT 10

References

algo.betweenness

Property Value

Procedure

algo.betweenness

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

1

Syntax

CALL algo.betweenness([{normalized: true}])
YIELD node, score

Parameters

Parameter Type Required Default Description

config map

Map

No

see defaults

Configuration properties (all optional)

normalized

Boolean

No

true

Divide scores by 2/n-1)(n-2 to normalize to [0,1]

Yield Fields

Field Type Description

node

RID

Vertex identity

score

Double

Betweenness centrality score

Description

Measures how often a vertex lies on the shortest path between all other pairs, using the Brandes algorithm with stack-based back-propagation. When normalized is true, scores are divided by 2/n-1)(n-2 (undirected normalization factor).

Use Cases

  • Identifying bridge nodes and bottlenecks in networks

  • Communication hub detection in social graphs

  • Critical infrastructure analysis

Example

CALL algo.betweenness({normalized: true})
YIELD node, score
RETURN node, score ORDER BY score DESC LIMIT 20

References

algo.closeness

Property Value

Procedure

algo.closeness

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

3

Syntax

CALL algo.closeness([relTypes, direction, normalized])
YIELD node, score

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

Traversal direction: "IN", "OUT", or "BOTH"

normalized

Boolean

No

true

Use Wasserman-Faust formula for disconnected graphs

Yield Fields

Field Type Description

node

RID

Vertex identity

score

Double

Closeness centrality score

Description

Computes closeness centrality via BFS from each vertex. For disconnected graphs, the Wasserman-Faust formula is applied: score = (reachable / sumDist) × (reachable / (n-1)), where reachable is the number of vertices reached and sumDist is the sum of shortest path distances to those vertices.

Use Cases

  • Identifying well-positioned nodes for information spread

  • Supply chain hub identification

  • Social network influence reach analysis

Example

CALL algo.closeness('KNOWS', 'BOTH', true)
YIELD node, score
RETURN node, score ORDER BY score DESC LIMIT 10

References

algo.degree

Property Value

Procedure

algo.degree

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

2

Syntax

CALL algo.degree([relTypes, direction])
YIELD node, inDegree, outDegree, degree, score

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

Traversal direction: "IN", "OUT", or "BOTH"

Yield Fields

Field Type Description

node

RID

Vertex identity

inDegree

Long

Number of incoming edges

outDegree

Long

Number of outgoing edges

degree

Long

Total degree (in + out for BOTH, else directional)

score

Double

Normalized degree: total / (n-1)

Description

Efficiently counts in-degree, out-degree, and total degree for every vertex using vertex.countEdges() to avoid materializing edge objects. The normalized score divides total degree by (n-1), representing the fraction of all possible connections.

Use Cases

  • Identifying high-degree hubs in social networks

  • Popularity ranking by connection count

  • Network connectivity baseline measurement

Example

CALL algo.degree('FOLLOWS', 'IN')
YIELD node, inDegree, score
RETURN node, inDegree, score ORDER BY inDegree DESC LIMIT 10

References

algo.harmonic

Property Value

Procedure

algo.harmonic

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

3

Syntax

CALL algo.harmonic([relTypes, direction, normalized])
YIELD node, score

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

Traversal direction: "IN", "OUT", or "BOTH"

normalized

Boolean

No

true

Divide raw score by (n-1)

Yield Fields

Field Type Description

node

RID

Vertex identity

score

Double

Harmonic centrality score

Description

Computes harmonic centrality as the sum of reciprocal shortest-path distances from a vertex to all reachable vertices: score = Σ 1/dist(v, u). When normalized is true, divides by (n-1). Harmonic centrality handles disconnected graphs naturally (unreachable vertices contribute 0 to the sum), unlike closeness centrality.

Use Cases

  • Centrality measure robust to disconnected components

  • Influence reach in sparse networks

  • Alternative to closeness in disconnected graphs

Example

CALL algo.harmonic('KNOWS', 'BOTH', true)
YIELD node, score
RETURN node, score ORDER BY score DESC LIMIT 10

References

algo.eigenvector

Property Value

Procedure

algo.eigenvector

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

4

Syntax

CALL algo.eigenvector([relTypes, direction, maxIterations, tolerance])
YIELD node, score

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

Traversal direction: "IN", "OUT", or "BOTH"

maxIterations

Integer

No

20

Maximum power-iteration steps

tolerance

Double

No

1e-6

Convergence threshold

Yield Fields

Field Type Description

node

RID

Vertex identity

score

Double

Eigenvector centrality score in [0, 1]

Description

Computes eigenvector centrality using the power iteration method. A node scores highly if it is connected to other high-scoring nodes. L∞ normalization (divide by maximum score) keeps values in [0, 1]. Convergence is checked against the maximum absolute change in scores between iterations.

Use Cases

  • Identifying globally influential nodes

  • Academic citation influence analysis

  • Prestige scoring in directed networks

Example

CALL algo.eigenvector('CITES', 'IN', 50, 1e-8)
YIELD node, score
RETURN node, score ORDER BY score DESC LIMIT 10

References

algo.hits

Property Value

Procedure

algo.hits

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

3

Syntax

CALL algo.hits([relTypes, maxIterations, tolerance])
YIELD node, hubScore, authorityScore

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

maxIterations

Integer

No

20

Maximum number of iterations

tolerance

Double

No

1e-6

Convergence threshold (max score change)

Yield Fields

Field Type Description

node

RID

Vertex identity

hubScore

Double

Hub score (good hub points to good authorities)

authorityScore

Double

Authority score (good authority is pointed to by good hubs)

Description

Computes Hyperlink-Induced Topic Search (HITS) scores using alternating updates: authority scores are the sum of hub scores of incoming neighbors; hub scores are the sum of authority scores of outgoing neighbors. Both score vectors are L2-normalized after each iteration.

Use Cases

  • Web link analysis (hubs = index pages, authorities = content pages)

  • Identifying experts vs. curators in knowledge networks

  • Bipartite influence analysis

Example

CALL algo.hits('LINKS_TO', 30, 1e-8)
YIELD node, hubScore, authorityScore
RETURN node, hubScore, authorityScore ORDER BY authorityScore DESC LIMIT 10

References

  • HITS algorithm – Wikipedia

  • Kleinberg, J. M. (1999). Authoritative sources in a hyperlinked environment. Journal of the ACM, 46(5), 604–632.

algo.katz

Property Value

Procedure

algo.katz

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

4

Syntax

CALL algo.katz([relTypes, alpha, maxIterations, tolerance])
YIELD nodeId, score

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

alpha

Double

No

0.005

Attenuation factor (must be less than 1/λ_max)

maxIterations

Integer

No

100

Maximum number of iterations

tolerance

Double

No

1e-6

Convergence threshold

Yield Fields

Field Type Description

nodeId

RID

Vertex identity

score

Double

Katz centrality score (normalized to [0, 1])

Description

Computes Katz centrality, which counts all paths between nodes with exponential decay by path length. Formula: k[i] = alpha × Σ_j(A[j][i] × k[j]) + 1, normalized by the maximum score. Unlike eigenvector centrality, every node receives a base score (the +1 term), making it robust for directed and sparse graphs.

Use Cases

  • Influence ranking in directed social networks

  • Ranking nodes when direct connection is sparse

  • Early-stage recommendation systems

Example

CALL algo.katz('FOLLOWS', 0.01, 50, 1e-8)
YIELD nodeId, score
RETURN nodeId, score ORDER BY score DESC LIMIT 10

References

algo.voteRank

Property Value

Procedure

algo.voteRank

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

2

Syntax

CALL algo.voteRank([relTypes, topK])
YIELD nodeId, rank

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

topK

Integer

No

all nodes

Maximum number of top spreaders to return

Yield Fields

Field Type Description

nodeId

RID

Vertex identity

rank

Integer

1-based rank (1 = most influential spreader)

Description

Identifies the most influential spreaders in a network using an iterative election process. In each round, the node with the highest accumulated votes is selected as a spreader. After selection, each of its neighbors has its voting ability reduced by 1/degree. This suppression mechanism ensures that the selected spreaders are structurally diverse rather than clustered together.

Use Cases

  • Viral marketing seed set selection

  • Identifying structurally independent influencers

  • Epidemic intervention: selecting individuals for immunization

Example

CALL algo.voteRank('KNOWS', 5)
YIELD nodeId, rank
RETURN nodeId, rank ORDER BY rank ASC

References

  • Zhang, J., et al. (2016). Identifying a set of influential spreaders in complex networks. Scientific Reports, 6, 27823.

algo.eccentricity

Property Value

Procedure

algo.eccentricity

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

2

Syntax

CALL algo.eccentricity([relTypes, direction])
YIELD node, eccentricity, isCenter, isPeripheral

Parameters

Parameter Type Required Default Description

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

Traversal direction: "IN", "OUT", or "BOTH"

Yield Fields

Field Type Description

node

RID

Vertex identity

eccentricity

Integer

Maximum shortest-path distance to any reachable vertex

isCenter

Boolean

true if eccentricity equals the graph radius

isPeripheral

Boolean

true if eccentricity equals the graph diameter

Description

Computes the eccentricity of each vertex (the greatest shortest-path distance to any other reachable vertex) via BFS from each node. The graph radius is the minimum eccentricity and the graph diameter is the maximum. Center nodes have eccentricity equal to the radius; peripheral nodes have eccentricity equal to the diameter.

Use Cases

  • Graph center identification for optimal facility placement

  • Network diameter and radius computation

  • Peripheral node analysis for vulnerability assessment

Example

CALL algo.eccentricity('ROAD', 'BOTH')
YIELD node, eccentricity, isCenter, isPeripheral
RETURN node, eccentricity, isCenter, isPeripheral ORDER BY eccentricity ASC

References

algo.personalizedPageRank

Property Value

Procedure

algo.personalizedPageRank

Category

Centrality

Complexity

CPU

Min Args

1

Max Args

5

Syntax

CALL algo.personalizedPageRank(sourceNode [, relTypes, dampingFactor, maxIterations, tolerance])
YIELD nodeId, score

Parameters

Parameter Type Required Default Description

sourceNode

Vertex

Yes

—

The personalization origin vertex

relTypes

String

No

all types

Comma-separated relationship types

dampingFactor

Double

No

0.85

Probability of following an edge

maxIterations

Integer

No

20

Maximum power-iteration steps

tolerance

Double

No

1e-6

Convergence threshold

Yield Fields

Field Type Description

nodeId

RID

Vertex identity

score

Double

Personalized PageRank score relative to the source node

Description

Computes Personalized PageRank (PPR) relative to a single source vertex. Unlike standard PageRank, the teleportation probability is concentrated entirely at the source node (personalization vector = 1 at source, 0 everywhere else). Scores represent structural proximity/importance relative to the source. Dangling nodes contribute their rank back to the source only.

Use Cases

  • Node-centric similarity and proximity ranking

  • Recommendation systems ("nodes similar to X")

  • Query-centric graph exploration

Example

MATCH (s:Person {name:'Alice'})
CALL algo.personalizedPageRank(s, 'KNOWS', 0.85, 20, 0.000001)
YIELD nodeId, score
RETURN nodeId, score ORDER BY score DESC LIMIT 10

References

algo.articlerank

Property Value

Procedure

algo.articlerank

Category

Centrality

Complexity

CPU

Min Args

0

Max Args

1

Syntax

CALL algo.articlerank([config]) YIELD node, score

Parameters

Name Type Default Description

config

Map

{}

Configuration map (see below)

Config Parameters

Key Type Default Description

dampingFactor

Float

0.85

Damping factor (probability of following a link)

maxIterations

Integer

20

Maximum number of iterations

tolerance

Float

0.0001

Convergence threshold (sum of absolute score changes)

Yield Fields

Field Type Description

node

Vertex

The vertex

score

Float

ArticleRank score for the vertex

Description

ArticleRank is a variant of PageRank that dampens the contribution of low-degree nodes. While standard PageRank divides a node’s rank equally among its out-degree neighbours, ArticleRank divides by outDegree(v) + avgOutDegree. This reduces the influence of nodes with very few connections, producing more balanced centrality scores in sparse or scale-free graphs.

Formula: AR(u) = (1 − d) / N + d × Σ AR(v) / (outDeg(v) + avgOutDeg)

Use Cases

  • Web page importance ranking where low-citation pages should have less influence

  • Academic citation networks with highly skewed degree distributions

  • Any domain where hub dampening is desirable

Example

CALL algo.articlerank({dampingFactor: 0.85, maxIterations: 20})
YIELD node, score
RETURN node.name AS name, score
ORDER BY score DESC LIMIT 10

References