Audit Shortest Paths and Reachability
Calculate distance only among reachable ordered pairs, make disconnected cases visible, and match path direction to the social process.
Method sources
By the end of this tutorial
- 1Define geodesic distance and reachability from an explicit node, tie, boundary, direction, weight, and observation-window specification.
- 2Apply and audit this procedure: Calculate directed shortest paths, enumerate unreachable ordered pairs, report component membership and harmonic rather than ordinary closeness when appropriate, and reverse edge direction only for a separately stated flow question.
- 3Interpret the result with a sensitivity check and the following evidence boundary: A short path is a potential structural route under the specified relation, not proof that information traveled, remained accurate, or reached someone quickly.
SNA
Network specification
Analysis scenario
A district wants to estimate how many advice steps separate teachers from curriculum expertise across a directed school network.
Nodes
All teachers and curriculum specialists eligible during the same eight-week advice window.
Ties
A directed link from a teacher to a person from whom that teacher sought substantive curriculum advice.
Network type
One-mode, directed, binary whole network with multiple components, retained isolates, no self-ties, and unknown nonresponse.
Step-by-step tutorial
Freeze the relational question
Write the decision the analysis must inform, then lock the eligible node roster, tie-generating event, direction, weight, self-tie rule, observation window, and missing-data code. Preserve a read-only source copy and record why this specification represents the stated question.
Checkpoint
A second analyst can reconstruct the same node set and edge table from the written rules without guessing what an absent record means.
Compute the focal structure
Work on a versioned analysis copy and carry out the focal method exactly as specified: Calculate directed shortest paths, enumerate unreachable ordered pairs, report component membership and harmonic rather than ordinary closeness when appropriate, and reverse edge direction only for a separately stated flow question. Save software and package versions, every threshold, normalization, seed, and intermediate count needed to reproduce the result.
Checkpoint
The output is tied to one named data version and includes the denominator, parameter settings, and a reproducible calculation record.
Run a structural sensitivity check
Repeat the analysis under at least one defensible alternative boundary, missingness rule, tie threshold, weight transformation, or model setting. Compare membership and substantive conclusions, not only a single coefficient, and investigate every change large enough to alter a decision.
Checkpoint
The audit states which patterns persist, which actors or groups change classification, and which conclusion depends on an analyst choice.
Report for responsible action
Pair the numerical result with a table or structure-preserving visual, document excluded and missing actors, and explain uncertainty in plain language. Convert the finding into a reversible support question, not an automatic ranking, while stating this boundary: A short path is a potential structural route under the specified relation, not proof that information traveled, remained accurate, or reached someone quickly.
Checkpoint
The final note contains the question, specification, result, sensitivity evidence, uncertainty, privacy controls, and a proportionate next step.
Interpret with care
geodesic distance and reachability describes a property of the specified relation and network boundary. It does not transfer automatically to another relation, time period, class, platform, or population.
A short path is a potential structural route under the specified relation, not proof that information traveled, remained accurate, or reached someone quickly. Compare the result with raw counts, missingness, plausible alternative specifications, and contextual evidence before acting.