Separate Node Centrality from Network Centralization
Distinguish an actor's position from the whole network's inequality around its most central position and keep the reference maximum visible.
Method sources
By the end of this tutorial
- 1Define centrality and network centralization from an explicit node, tie, boundary, direction, weight, and observation-window specification.
- 2Apply and audit this procedure: Calculate actor in-degree or another stated centrality, compute graph centralization as the normalized sum of gaps from the maximum, show the theoretical reference graph, and compare departments only under matched size and measurement.
- 3Interpret the result with a sensitivity check and the following evidence boundary: A high-centrality actor and a highly centralized network are different claims; neither alone proves dependence, expertise, hierarchy, resilience, or performance.
SNA
Network specification
Analysis scenario
Two departments each have a coordinator with in-degree 12, but one network distributes advice broadly while the other depends heavily on that coordinator.
Nodes
All staff in each department under the same census-date inclusion rule.
Ties
A directed report that one staff member sought substantive work advice from another during the last month.
Network type
Two comparable one-mode directed binary whole networks with complete rosters, retained isolates, and identical tie wording.
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 actor in-degree or another stated centrality, compute graph centralization as the normalized sum of gaps from the maximum, show the theoretical reference graph, and compare departments only under matched size and measurement. 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 high-centrality actor and a highly centralized network are different claims; neither alone proves dependence, expertise, hierarchy, resilience, or performance.
Checkpoint
The final note contains the question, specification, result, sensitivity evidence, uncertainty, privacy controls, and a proportionate next step.
Interpret with care
centrality and network centralization 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 high-centrality actor and a highly centralized network are different claims; neither alone proves dependence, expertise, hierarchy, resilience, or performance. Compare the result with raw counts, missingness, plausible alternative specifications, and contextual evidence before acting.