Compare Assortativity and the E-I Index
Use two normalized views of group mixing, inspect their denominators, and avoid interpreting either coefficient without the mixing table.
Method sources
By the end of this tutorial
- 1Define categorical assortativity and the external-internal index from an explicit node, tie, boundary, direction, weight, and observation-window specification.
- 2Apply and audit this procedure: Calculate the full directed mixing matrix, categorical assortativity, and group-specific plus overall E-I indices, then compare them with degree-preserving permutations and group-size diagnostics.
- 3Interpret the result with a sensitivity check and the following evidence boundary: Assortativity and E-I use different normalizations and can disagree under unequal groups or degree patterns; neither coefficient identifies why boundaries exist.
SNA
Network specification
Analysis scenario
A student-governance review asks whether working relations connect six committees or remain inside them despite sharply unequal committee sizes.
Nodes
All eligible office holders across the six governance committees at the review date.
Ties
A directed report that one office holder coordinated a substantive governance task with another during the semester.
Network type
One-mode, directed, binary whole network with committee as a categorical attribute, no self-ties, and retained nonrespondent status.
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 the full directed mixing matrix, categorical assortativity, and group-specific plus overall E-I indices, then compare them with degree-preserving permutations and group-size diagnostics. 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: Assortativity and E-I use different normalizations and can disagree under unequal groups or degree patterns; neither coefficient identifies why boundaries exist.
Checkpoint
The final note contains the question, specification, result, sensitivity evidence, uncertainty, privacy controls, and a proportionate next step.
Interpret with care
categorical assortativity and the external-internal index describes a property of the specified relation and network boundary. It does not transfer automatically to another relation, time period, class, platform, or population.
Assortativity and E-I use different normalizations and can disagree under unequal groups or degree patterns; neither coefficient identifies why boundaries exist. Compare the result with raw counts, missingness, plausible alternative specifications, and contextual evidence before acting.