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.
Description
Characteristic path length needs a convention for disconnected nodes.
Characteristic path length needs a convention for disconnected nodes. This tool averages only finite shortest paths while reporting how many unordered pairs are disconnected.
The tool returns meanConnectedPathLength (mean connected path length); connectedPairCount (connected pair count); disconnectedPairCount (disconnected pair count); allPairsConnected (all pairs connected). 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 Path Length
Use Network Path Length when you already have adjacency and want meanConnectedPathLength, connectedPairCount, disconnectedPairCount, allPairsConnected. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Network Path Length 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 meanConnectedPathLength, connectedPairCount, disconnectedPairCount, allPairsConnected. 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 |
Compute all-pairs shortest paths in a binary undirected loop-free graph. Count each unordered pair once; no connected pairs gives a zero mean with separate counts.
mean path = Σfinite shortest distances / connectedPairCount 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": {
"meanConnectedPathLength": 1.3333333333333333,
"connectedPairCount": 3,
"disconnectedPairCount": 0,
"allPairsConnected": true
}
}Limitations and assumptions
Zero is a sentinel for an empty connected-pair set. Excluding disconnected pairs can make sparse graphs appear to have short paths.
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. 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
- Global Network Efficiency
Compute mean reciprocal shortest-path distance over ordered node pairs, assigning disconnected pairs zero contribution in a binary undirected graph.
- 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.