Global Network Efficiency
Compute mean reciprocal shortest-path distance over ordered node pairs, assigning disconnected pairs zero contribution in a binary undirected graph.
Description
Global network efficiency averages reciprocal shortest-path lengths.
Global network efficiency averages reciprocal shortest-path lengths. Disconnected pairs contribute zero rather than forcing an infinite mean path length.
The tool returns globalEfficiency (global 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 Global Network Efficiency
Use Global Network Efficiency when you already have adjacency and want globalEfficiency. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Global 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 globalEfficiency. 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 adjacency matrix with zero diagonal. Compute all-pairs paths and average over ordered distinct pairs, with 1/∞ defined as zero.
efficiency = Σi≠j 1/dᵢⱼ / (N(N−1)) 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,
0
],
[
1,
0,
1
],
[
0,
1,
0
]
]
},
"output": {
"globalEfficiency": 0.8333333333333334
}
}Limitations and assumptions
The graph is unweighted and undirected. This does not infer a network from recordings or test differences between groups.
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
Network Path Length: Calculate mean shortest path over connected unordered pairs and report excluded disconnected pairs; zero mean with zero connected pairs is an explicit empty-pair result. 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.
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
- Network Path Length
Calculate mean shortest path over connected unordered pairs and report excluded disconnected pairs; zero mean with zero connected pairs is an explicit empty-pair result.
- 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.