Similarity and Link Prediction

algo.jaccard

Property Value

Procedure

algo.jaccard

Category

Similarity

Complexity

CPU

Min Args

1

Max Args

4

Syntax

CALL algo.jaccard(node [, relTypes, direction, cutoff])
YIELD node1, node2, similarity

Parameters

Parameter Type Required Default Description

node

Vertex

Yes

—

Source vertex to compare against all others

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

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

cutoff

Double

No

0.0

Minimum similarity threshold; pairs below are excluded

Yield Fields

Field Type Description

node1

RID

Source vertex identity

node2

RID

Compared vertex identity

similarity

Double

Jaccard similarity: |N(src) ∩ N(v)| / |N(src) ∪ N(v)|

Description

Computes the Jaccard similarity between the given source vertex and all other vertices, based on neighborhood overlap. Formula: similarity = |N(src) ∩ N(v)| / |N(src) ∪ N(v)|. Pairs with similarity below cutoff are filtered out.

Use Cases

  • Collaborative filtering: "users with similar tastes"

  • Friend recommendation based on shared connections

  • Document similarity via shared keyword links

Example

MATCH (u:User {name:'Alice'})
CALL algo.jaccard(u, 'LIKES', 'OUT', 0.2)
YIELD node1, node2, similarity
RETURN node2, similarity ORDER BY similarity DESC LIMIT 10

References

algo.adamicAdar

Property Value

Procedure

algo.adamicAdar

Category

Link Prediction

Complexity

CPU

Min Args

1

Max Args

4

Syntax

CALL algo.adamicAdar(node [, relTypes, direction, cutoff])
YIELD node1, node2, score

Parameters

Parameter Type Required Default Description

node

Vertex

Yes

—

Source vertex

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

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

cutoff

Double

No

0.0

Minimum score threshold

Yield Fields

Field Type Description

node1

RID

Source vertex identity

node2

RID

Compared vertex identity

score

Double

Adamic-Adar score; higher = more likely to form a link

Description

Computes the Adamic-Adar link prediction score between the source vertex and all non-adjacent vertices. For each pair, the score is the sum over common neighbors w of 1/log(degree(w)). Highly-connected common neighbors contribute less than rare common neighbors. Results are sorted by score descending.

Use Cases

  • Social network friend recommendation

  • Knowledge graph link prediction

  • Co-authorship prediction in citation networks

Example

MATCH (p:Person {name:'Bob'})
CALL algo.adamicAdar(p, 'KNOWS', 'BOTH', 0.5)
YIELD node1, node2, score
RETURN node2, score ORDER BY score DESC LIMIT 10

References

  • Adamic, L. & Adar, E. (2003). Friends and neighbors on the web. Social Networks, 25(3), 211–230.

algo.commonNeighbors

Property Value

Procedure

algo.commonNeighbors

Category

Link Prediction

Complexity

CPU

Min Args

1

Max Args

4

Syntax

CALL algo.commonNeighbors(node [, relTypes, direction, cutoff])
YIELD node1, node2, commonNeighbors

Parameters

Parameter Type Required Default Description

node

Vertex

Yes

—

Source vertex

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

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

cutoff

Integer

No

1

Minimum number of common neighbors

Yield Fields

Field Type Description

node1

RID

Source vertex identity

node2

RID

Compared vertex identity

commonNeighbors

Integer

Count of shared neighbors

Description

Counts the number of common neighbors between the source vertex and all other vertices. Pairs with fewer than cutoff common neighbors are excluded. Results are sorted by count descending.

Use Cases

  • Simple friend-of-a-friend recommendation

  • Link prediction baseline

  • Mutual connection analysis

Example

MATCH (u:User {name:'Charlie'})
CALL algo.commonNeighbors(u, 'FOLLOWS', 'BOTH', 3)
YIELD node1, node2, commonNeighbors
RETURN node2, commonNeighbors ORDER BY commonNeighbors DESC LIMIT 10

References

algo.preferentialAttachment

Property Value

Procedure

algo.preferentialAttachment

Category

Link Prediction

Complexity

CPU

Min Args

1

Max Args

3

Syntax

CALL algo.preferentialAttachment(node [, relTypes, direction])
YIELD node1, node2, score

Parameters

Parameter Type Required Default Description

node

Vertex

Yes

—

Source vertex

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

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

Yield Fields

Field Type Description

node1

RID

Source vertex identity

node2

RID

Compared vertex identity

score

Long

Product of the two nodes' degrees

Description

Computes the preferential attachment score for each pair as degree(node1) × degree(node2). Based on the observation that in evolving networks, new links preferentially form between high-degree nodes. A simple but effective baseline for link prediction in scale-free networks.

Use Cases

  • Scale-free network link prediction

  • Social network "people you may know" baseline

  • Network growth modeling

Example

MATCH (u:User {id:1})
CALL algo.preferentialAttachment(u, 'KNOWS', 'BOTH')
YIELD node1, node2, score
RETURN node2, score ORDER BY score DESC LIMIT 10

References

algo.resourceAllocation

Property Value

Procedure

algo.resourceAllocation

Category

Link Prediction

Complexity

CPU

Min Args

1

Max Args

4

Syntax

CALL algo.resourceAllocation(node [, relTypes, direction, cutoff])
YIELD node1, node2, score

Parameters

Parameter Type Required Default Description

node

Vertex

Yes

—

Source vertex

relTypes

String

No

all types

Comma-separated relationship types

direction

String

No

"BOTH"

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

cutoff

Double

No

0.0

Minimum score threshold

Yield Fields

Field Type Description

node1

RID

Source vertex identity

node2

RID

Compared vertex identity

score

Double

Resource allocation score

Description

Computes the resource allocation link prediction score: score = Σ 1/degree(w) over all common neighbors w. Models the fraction of "resources" that each common neighbor can send to both endpoints if it distributes equally to all its neighbors. Conceptually similar to Adamic-Adar but uses degree directly rather than its logarithm.

Use Cases

  • Link prediction with emphasis on rare intermediaries

  • Recommendation in sparse networks

  • Metabolic network pathway prediction

Example

MATCH (p:Protein {id:'P1'})
CALL algo.resourceAllocation(p, 'INTERACTS', 'BOTH', 0.1)
YIELD node1, node2, score
RETURN node2, score ORDER BY score DESC LIMIT 10

References

  • Zhou, T., Lü, L., & Zhang, Y. C. (2009). Predicting missing links via local information. European Physical Journal B, 71(4), 623–630.

algo.simRank

Property Value

Procedure

algo.simRank

Category

Similarity

Complexity

CPU+RAM

Min Args

2

Max Args

5

Syntax

CALL algo.simRank(nodeA, nodeB [, relTypes, decayFactor, maxIterations])
YIELD similarity, nodeAId, nodeBId

Parameters

Parameter Type Required Default Description

nodeA

Vertex

Yes

—

First vertex

nodeB

Vertex

Yes

—

Second vertex

relTypes

String

No

all types

Comma-separated relationship types

decayFactor

Double

No

0.8

Decay constant C ∈ (0,1)

maxIterations

Integer

No

5

Number of refinement iterations

Yield Fields

Field Type Description

similarity

Double

SimRank similarity score between nodeA and nodeB

nodeAId

RID

Identity of nodeA

nodeBId

RID

Identity of nodeB

Description

Computes SimRank similarity between two vertices using the recursive definition: two nodes are similar if they are pointed to by similar nodes. Maintains a full V×V similarity matrix (O(V²) memory), updated iteratively. Similarity of a node with itself is 1.0. Uses IN adjacency for the standard directed graph formulation.

Use Cases

  • Structural equivalence analysis in directed graphs

  • Computing vertex pair similarity for matching problems

  • Entity resolution in knowledge graphs

Example

MATCH (a:Paper {id:'P1'}), (b:Paper {id:'P2'})
CALL algo.simRank(a, b, 'CITES', 0.8, 5)
YIELD similarity, nodeAId, nodeBId
RETURN nodeAId, nodeBId, similarity

References

  • Jeh, G. & Widom, J. (2002). SimRank: a measure of structural-context similarity. KDD 2002.

algo.knn

Property Value

Procedure

algo.knn

Category

Similarity

Complexity

CPU

Min Args

0

Max Args

3

Syntax

CALL algo.knn([k, relTypes, direction]) YIELD node1, node2, similarity

Parameters

Name Type Default Description

k

Integer

5

Number of nearest neighbours to return per node

relTypes

String

all types

Comma-separated edge type names to consider

direction

String

"BOTH"

Edge traversal direction: IN, OUT, or BOTH

Yield Fields

Field Type Description

node1

Vertex

Source vertex

node2

Vertex

One of the k nearest neighbours of node1

similarity

Float

Jaccard similarity score in [0.0, 1.0]

Description

Constructs a k-Nearest Neighbours (KNN) graph using Jaccard similarity on neighbourhood sets. For each pair of nodes, the similarity is computed as |N(u) ∩ N(v)| / |N(u) ∪ N(v)|. Each node retains only its top-k neighbours by similarity score. This produces a new graph representing approximate structural proximity, useful as a pre-processing step for community detection or recommendation.

Use Cases

  • Constructing similarity graphs for downstream community detection

  • Collaborative filtering and recommendation

  • Detecting structurally similar entities (users, documents, products)

Example

CALL algo.knn(10, 'KNOWS', 'BOTH')
YIELD node1, node2, similarity
RETURN node1.name AS source, node2.name AS neighbour, similarity
ORDER BY source, similarity DESC

References

algo.sameCommunity

Property Value

Procedure

algo.sameCommunity

Category

Link Prediction

Complexity

CPU

Min Args

3

Max Args

3

Syntax

CALL algo.sameCommunity(node1, node2, communityProperty) YIELD node1, node2, coefficient

Parameters

Name Type Default Description

node1

Vertex

—

First vertex

node2

Vertex

—

Second vertex

communityProperty

String

—

Property name holding the community identifier on each vertex

Yield Fields

Field Type Description

node1

Vertex

The first vertex

node2

Vertex

The second vertex

coefficient

Float

1.0 if both nodes share the same community value, 0.0 otherwise

Description

A simple link-prediction feature: returns 1.0 when both nodes carry the same value for the given community property and 0.0 otherwise. Useful as a binary feature in machine-learning pipelines or to filter / weight edges based on community membership.

Use Cases

  • Feature engineering for link-prediction models

  • Filtering candidate edges to intra-community connections

  • Evaluating community detection quality (ground-truth comparison)

Example

MATCH (a:Person), (b:Person)
WHERE a <> b
CALL algo.sameCommunity(a, b, 'community')
YIELD coefficient
WHERE coefficient = 1.0
RETURN a.name, b.name

References

algo.totalNeighbors

Property Value

Procedure

algo.totalNeighbors

Category

Link Prediction

Complexity

CPU

Min Args

2

Max Args

4

Syntax

CALL algo.totalNeighbors(node1, node2 [, relTypes, direction]) YIELD node1, node2, coefficient

Parameters

Name Type Default Description

node1

Vertex

—

First vertex

node2

Vertex

—

Second vertex

relTypes

String

all types

Comma-separated edge type names to traverse

direction

String

"BOTH"

Edge traversal direction: IN, OUT, or BOTH

Yield Fields

Field Type Description

node1

Vertex

The first vertex

node2

Vertex

The second vertex

coefficient

Long

Size of the union of the two neighbourhood sets

Description

Computes |N(u) ∪ N(v)| — the total number of distinct neighbours across both nodes. This is the denominator of Jaccard similarity and is used as a link-prediction feature measuring total neighbourhood reach. Calculated as |N(u)| + |N(v)| − |N(u) ∩ N(v)| using a BitSet intersection.

Use Cases

  • Feature engineering for link-prediction models

  • Identifying node pairs with large combined reach

  • Pre-filtering candidates before more expensive similarity computation

Example

MATCH (a:Person {name: 'Alice'}), (b:Person {name: 'Bob'})
CALL algo.totalNeighbors(a, b, 'KNOWS', 'BOTH')
YIELD coefficient
RETURN coefficient AS totalNeighbours

References