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.
Description
Local network efficiency evaluates how well a node’s neighbors connect to each other after excluding that node.
Local network efficiency evaluates how well a node’s neighbors connect to each other after excluding that node. It uses shortest paths inside each neighbor-induced subgraph.
The tool returns nodeLocalEfficiencies (node local efficiencies); meanLocalEfficiency (mean local efficiency). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Local Network Efficiency
Use Local Network Efficiency when you already have adjacency and want nodeLocalEfficiencies, meanLocalEfficiency. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Local Network Efficiency 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 nodeLocalEfficiencies, meanLocalEfficiency. 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 undirected loop-free graph with at most 32 nodes. Nodes with fewer than two neighbors get zero; disconnected neighbor pairs contribute zero. Average across all nodes.
local efficiency = mean(1/distance among ordered distinct neighbor pairs) 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": {
"nodeLocalEfficiencies": [
1,
1,
1
],
"meanLocalEfficiency": 1
}
}Limitations and assumptions
This is the binary induced-subgraph convention, not a weighted network measure or path calculation through the removed node.
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
Global Network Efficiency: Compute mean reciprocal shortest-path distance over ordered node pairs, assigning disconnected pairs zero contribution in a binary undirected graph. Network Clustering Coefficient: Compute local clustering, mean including degree<2 zero coefficients, and global transitivity for a binary undirected simple graph.
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
- Global Network Efficiency
Compute mean reciprocal shortest-path distance over ordered node pairs, assigning disconnected pairs zero contribution in a binary undirected graph.
- Network Clustering Coefficient
Compute local clustering, mean including degree<2 zero coefficients, and global transitivity for a binary undirected simple graph.