Network Science Metrics

algo.assortativity

Property Value

Property	Value
Procedure	`algo.assortativity`
Category	Network Science
Complexity	CPU
Min Args	0
Max Args	1

Procedure

algo.assortativity

Category

Network Science

Complexity

CPU

Min Args

Max Args

Syntax

CALL algo.assortativity([relTypes])
YIELD assortativity, edgeCount

Parameters

Parameter Type Required Default Description

Parameter	Type	Required	Default	Description
`relTypes`	String	No	all types	Comma-separated relationship types

relTypes

String

all types

Comma-separated relationship types

Yield Fields

Field Type Description

Field	Type	Description
`assortativity`	Double	Newman’s degree assortativity coefficient ∈ [-1, 1]
`edgeCount`	Integer	Number of edges used in the computation

assortativity

Double

Newman’s degree assortativity coefficient ∈ [-1, 1]

edgeCount

Integer

Number of edges used in the computation

Description

Computes Newman’s degree assortativity coefficient. A positive value indicates that high-degree nodes tend to connect to other high-degree nodes (assortative); negative indicates disassortative mixing.

Use Cases

Network topology characterization
Social network analysis (social networks are typically assortative)
Comparing mixing patterns across different networks

Example

CALL algo.assortativity('KNOWS')
YIELD assortativity, edgeCount
RETURN assortativity, edgeCount

References

Newman, M. E. J. (2002). Assortative mixing in networks. Physical Review Letters, 89(20), 208701.

algo.richClub

Property Value

Property	Value
Procedure	`algo.richClub`
Category	Network Science
Complexity	CPU
Min Args	0
Max Args	2

Procedure

algo.richClub

Category

Network Science

Complexity

CPU

Min Args

Max Args

Syntax

CALL algo.richClub([relTypes, minDegree])
YIELD degree, richClubCoefficient, nodeCount, edgeCount

Parameters

Parameter Type Required Default Description

Parameter	Type	Required	Default	Description
`relTypes`	String	No	all types	Comma-separated relationship types
`minDegree`	Integer	No	`2`	Starting degree threshold

relTypes

String

all types

Comma-separated relationship types

minDegree

Integer

2

Starting degree threshold

Yield Fields

Field Type Description

Field	Type	Description
`degree`	Integer	Degree threshold k for this row
`richClubCoefficient`	Double	φ(k): density of edges among nodes with degree > k
`nodeCount`	Integer	Number of nodes with degree > k
`edgeCount`	Integer	Number of edges among those nodes

degree

Integer

Degree threshold k for this row

richClubCoefficient

Double

φ(k): density of edges among nodes with degree > k

nodeCount

Integer

Number of nodes with degree > k

edgeCount

Integer

Number of edges among those nodes

Description

Computes the rich-club coefficient φ(k) for every degree threshold k from minDegree to the maximum degree in the graph. One row is returned per degree threshold. Formula: φ(k) = 2·E_k / (N_k·(N_k−1)), where N_k = number of nodes with degree > k and E_k = edges between those nodes.

Use Cases

Characterizing the "rich get richer" phenomenon
Network topology analysis: do high-degree nodes interconnect?
Comparing network structure across domains

Example

CALL algo.richClub('KNOWS', 2)
YIELD degree, richClubCoefficient, nodeCount, edgeCount
RETURN degree, richClubCoefficient ORDER BY degree ASC

References

Colizza, V., Flammini, A., Serrano, M. A., & Vespignani, A. (2006). Detecting rich-club ordering in complex networks. Nature Physics, 2, 110–115.

algo.influenceMaximization

Property Value

Property	Value
Procedure	`algo.influenceMaximization`
Category	Network Science
Complexity	CPU
Min Args	1
Max Args	4

Procedure

algo.influenceMaximization

Category

Network Science

Complexity

CPU

Min Args

Max Args

Syntax

CALL algo.influenceMaximization(k [, relTypes, simulations, propagationProbability])
YIELD nodeId, rank, marginalGain

Parameters

Parameter Type Required Default Description

Parameter	Type	Required	Default	Description
`k`	Integer	Yes	—	Number of seed nodes to select
`relTypes`	String	No	all types	Comma-separated relationship types
`simulations`	Integer	No	`100`	Monte Carlo simulation count per candidate
`propagationProbability`	Double	No	`0.1`	Independent Cascade activation probability per edge

k

Integer

Yes

—

Number of seed nodes to select

relTypes

String

all types

Comma-separated relationship types

simulations

Integer

100

Monte Carlo simulation count per candidate

propagationProbability

Double

0.1

Independent Cascade activation probability per edge

Yield Fields

Field Type Description

Field	Type	Description
`nodeId`	RID	Vertex identity of the selected seed node
`rank`	Integer	Selection rank (1 = best seed)
`marginalGain`	Double	Expected additional nodes activated by adding this seed

nodeId

RID

Vertex identity of the selected seed node

rank

Integer

Selection rank (1 = best seed)

marginalGain

Double

Expected additional nodes activated by adding this seed

Description

Selects k seed nodes that maximize influence spread using a greedy algorithm with Monte Carlo simulation of the Independent Cascade (IC) model. In each round, the candidate that maximizes the expected spread when added to the current seed set is selected.

Use Cases

Viral marketing campaign planning
Identifying optimal vaccination targets for epidemic control
Information cascade maximization in social media

Example

CALL algo.influenceMaximization(3, 'FOLLOWS', 200, 0.15)
YIELD nodeId, rank, marginalGain
RETURN nodeId, rank, marginalGain ORDER BY rank ASC

References

Kempe, D., Kleinberg, J., & Tardos, E. (2003). Maximizing the spread of influence through a social network. KDD 2003.