Design Network Null Models
State what randomization preserves before claiming that a cluster, motif, rich club, or repeated tie occurs more often than expected.
Method sources
By the end of this tutorial
- 1Define network null models and constrained randomization from an explicit node, tie, boundary, direction, weight, and observation-window specification.
- 2Apply and audit this procedure: Write the null hypothesis, choose whether to preserve node count, edge count, in-degree, out-degree, weights, reciprocity, or time, generate enough randomized graphs, and locate the observed statistic in the reference distribution.
- 3Interpret the result with a sensitivity check and the following evidence boundary: A surprising statistic is relative to one preservation rule; a poorly matched null can manufacture significance and does not reveal a causal mechanism.
SNA
Network specification
Analysis scenario
An online course appears to contain an unusually tight active-student core, and the team wants to know whether degree alone explains it.
Nodes
All students eligible for the semester discussion network, with the same roster used in observed and simulated graphs.
Ties
Directed replies between students, optionally weighted by frequency, with instructor messages excluded under the declared rule.
Network type
One-mode directed discussion network paired with an ensemble of randomized reference graphs.
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: Write the null hypothesis, choose whether to preserve node count, edge count, in-degree, out-degree, weights, reciprocity, or time, generate enough randomized graphs, and locate the observed statistic in the reference distribution. 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 surprising statistic is relative to one preservation rule; a poorly matched null can manufacture significance and does not reveal a causal mechanism.
Checkpoint
The final note contains the question, specification, result, sensitivity evidence, uncertainty, privacy controls, and a proportionate next step.
Interpret with care
network null models and constrained randomization 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 surprising statistic is relative to one preservation rule; a poorly matched null can manufacture significance and does not reveal a causal mechanism. Compare the result with raw counts, missingness, plausible alternative specifications, and contextual evidence before acting.