Compare Density, Reciprocity, and Transitivity
Turn a bounded directed network into three whole-network measures, state each denominator and convention, and interpret connection, mutual exchange, and triadic closure as distinct structural patterns.
Method sources
By the end of this tutorial
- 1Calculate density from observed and possible ties without dropping eligible isolates.
- 2Distinguish mutual dyads from transitive triads and state the convention used for each measure.
- 3Compare whole-network measures without treating cohesion as learning quality, trust, or causal influence.
SNA
Network specification
Analysis scenario
An instructor reviews peer replies among 18 students during a six-week online seminar. The roster includes students who never posted, instructor messages are excluded, and a tie records at least one direct student reply. The team wants to describe whether interaction is widespread, mutual, and locally closed before changing the discussion design.
Nodes
All 18 students enrolled on the seminar census date, including eligible students with no recorded outgoing or incoming reply during the six-week observation window.
Ties
A directed tie from student A to student B when A posted at least one direct reply to B during the six-week unit; repeated replies are collapsed to one binary tie and self-replies are removed.
Network type
One-mode, directed, unweighted whole network with a fixed course-roster boundary, one six-week observation window, no self-ties, instructors excluded, and missing platform records documented separately from observed zero ties.
Step-by-step tutorial
Freeze the network specification
Start from the node roster and edge list prepared in the earlier Academy lessons. Add every eligible student to the node table, remove self-replies and instructor activity, collapse repeated student-to-student replies to binary ties, and record the observation window and any missing export dates before calculating a measure.
Checkpoint
The adjacency matrix contains all 18 eligible students, its diagonal is zero, and a zero cell means an observed absence under the stated rule rather than an unknown record.
Calculate directed density
Count the observed directed ties m and divide by n(n-1), the number of possible directed non-self ties. With 18 students the denominator is 18 times 17, or 306. Report the observed tie count beside the proportion so readers can audit the numerator and understand the boundary.
Checkpoint
Density is between 0 and 1, uses 306 possible ties, retains isolates in n, and is not divided by the smaller undirected denominator n(n-1)/2.
Separate reciprocity from transitivity
For reciprocity, count mutual dyads and divide by all dyads with at least one observed tie, explicitly naming this dyad-based convention. For transitivity, count directed two-paths A to B to C that are closed by A to C and divide by all eligible directed two-paths with three distinct students.
Checkpoint
The worksheet shows the raw mutual-dyad and closed-two-path counts, and the same ordered pair or triad rules are used in every comparison network.
Interpret and stress-test the three measures
Describe density as tie prevalence, reciprocity as mutual exchange under the chosen convention, and transitivity as local closure. Recalculate after a defensible alternative such as requiring two replies per tie or excluding an incomplete export week, then explain which conclusions persist and which depend on measurement choices.
Checkpoint
The final interpretation names the boundary, time window, tie threshold, and formula conventions, reports sensitivity results, and makes no claim that a larger value caused better learning.
Interpret with care
The three measures answer different questions. A sparse directed network can still contain a high share of mutual dyads or closed two-paths, while a dense network can distribute many ties without making every exchange mutual. Never substitute one measure for an undefined idea of overall cohesion.
Values depend on who was eligible, which interactions counted, how repeated replies were collapsed, and the exact reciprocity and transitivity definitions. Comparisons are most credible when networks share the same boundary and observation opportunity or when differences are explicitly adjusted and stress-tested.