Community Quality Metrics

algo.modularityScore

Property Value

Procedure

algo.modularityScore

Category

Community Quality

Complexity

CPU

Min Args

1

Max Args

2

Syntax

CALL algo.modularityScore(communityProperty [, relTypes])
YIELD modularity, communities, edgeCount

Parameters

Parameter Type Required Default Description

communityProperty

String

Yes

—

Vertex property name holding the community label

relTypes

String

No

all types

Comma-separated relationship types

Yield Fields

Field Type Description

modularity

Double

Newman-Girvan modularity Q ∈ [-0.5, 1]

communities

Integer

Number of distinct communities found

edgeCount

Long

Total number of edges in the graph

Description

Evaluates the modularity of an existing community partition stored as a vertex property. Formula: Q = Σ_c [ L_c/m − (d_c/(2m))² ], where L_c is the number of internal edges in community c, d_c is the sum of degrees in c, and m is the total number of edges. Returns a single row.

Use Cases

  • Evaluating the output of community detection algorithms

  • Comparing alternative community assignments

  • Graph partition quality benchmarking

Example

CALL algo.modularityScore('community', 'KNOWS')
YIELD modularity, communities, edgeCount
RETURN modularity, communities, edgeCount

References

  • Newman, M. E. J. & Girvan, M. (2004). Finding and evaluating community structure in networks. Physical Review E, 69(2), 026113.

algo.conductance

Property Value

Procedure

algo.conductance

Category

Community Quality

Complexity

CPU

Min Args

1

Max Args

2

Syntax

CALL algo.conductance(communityProperty [, relTypes])
YIELD community, conductance, internalEdges, boundaryEdges, nodeCount

Parameters

Parameter Type Required Default Description

communityProperty

String

Yes

—

Vertex property name holding the community label

relTypes

String

No

all types

Comma-separated relationship types

Yield Fields

Field Type Description

community

Object

Community label value

conductance

Double

Conductance score (lower = better community)

internalEdges

Integer

Edges with both endpoints inside the community

boundaryEdges

Integer

Edges crossing the community boundary

nodeCount

Integer

Number of nodes in the community

Description

Computes the conductance of each community in an existing partition stored as a vertex property. Formula: conductance = cut© / min(vol©, vol(V\C)), where cut© is the number of boundary edges and vol© is the sum of degrees within C. Lower conductance indicates a better-separated community. Returns one row per community.

Use Cases

  • Evaluating community separation quality

  • Identifying poorly-separated or "leaky" communities

  • Graph cut analysis for partitioning algorithms

Example

CALL algo.conductance('community', 'KNOWS')
YIELD community, conductance, internalEdges, boundaryEdges, nodeCount
RETURN community, conductance ORDER BY conductance ASC

References