Network Clustering Coefficient
Compute local clustering, mean including degree<2 zero coefficients, and global transitivity for a binary undirected simple graph.
Description
Binary network clustering describes links among a node’s neighbors.
Binary network clustering describes links among a node’s neighbors. Mean local clustering and network transitivity use different weights.
The tool returns localCoefficients (local coefficients); meanLocalCoefficient (mean local coefficient); transitivity (transitivity). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Network Clustering Coefficient
Use Network Clustering Coefficient when you already have adjacency and want localCoefficients, meanLocalCoefficient, transitivity. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Network Clustering Coefficient and understand its results
- Enter adjacency using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read localCoefficients, meanLocalCoefficient, transitivity. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| adjacency | Adjacency | list of list of number | Required |
Use a binary symmetric loop-free graph. Nodes with fewer than two neighbors contribute zero to the mean; zero total triples gives zero transitivity.
local = neighborLinks/possibleNeighborPairs; transitivity = ΣneighborLinks/ΣpossibleNeighborPairs The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"adjacency": [
[
0,
1,
1
],
[
1,
0,
1
],
[
1,
1,
0
]
]
},
"output": {
"localCoefficients": [
1,
1,
1
],
"meanLocalCoefficient": 1,
"transitivity": 1
}
}Limitations and assumptions
The graph is supplied and unweighted. These summaries are not equivalent and provide no reference normalization or significance test.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Local Network Efficiency: Calculate efficiency within each node’s induced neighbor subgraph for 2–32 nodes; degree<2 nodes contribute zero and paths cannot pass through the removed central node. Small World Index: Normalize observed clustering and characteristic path length against caller-generated matched reference graphs; no random-graph null or universal small-world label is invented.
Methodological background: Complex network measures of brain connectivity: uses and interpretations.1
References
-
Complex network measures of brain connectivity: uses and interpretations — Rubinov and Sporns; NeuroImage
Similar or alternative tools
- Local Network Efficiency
Calculate efficiency within each node’s induced neighbor subgraph for 2–32 nodes; degree<2 nodes contribute zero and paths cannot pass through the removed central node.
- Small World Index
Normalize observed clustering and characteristic path length against caller-generated matched reference graphs; no random-graph null or universal small-world label is invented.