nwtriads

Triad census of a network

Syntax

nwtriads
[netname]
[,
plot
name(string)]

plot	Draw a bar chart of the 16 MAN-category counts
name(string)	Name for the graph created by plot; default = triads

Description

Returns the triad census of the network (or a list of networks). This is a way to characertize a network based on its triads.

Each unique triad (triple of nodes i, j, and k) in a directed network can be one of the following:

• 003 = i,j,k, empty triad.
• 012 = i->j, k, triad with a single directed edge.
• 102 = i<->j, k, triad with a reciprocated connection between two vertices.
• 021D = i<-j->k, triadic out-star.
• 021U = i->j<-k triadic in-star.
• 021C = i->j->k, directed line.
• 111D = i<->j<-k
• 111U = i<->j->k.
• 030T = i->j<-k, i->k.
• 030C = i<-j<-k, i->k.
• 201 = i<->j<->k.
• 120D = i<-j->k, i<->k.
• 120U = i->j<-k, i<->k.
• 120C = i->j->k, i<->k.
• 210 = i->j<->k, i<->k.
• 300 = i<->j<->k, i<->k, complete triad.

This is the so called MAN notation. As in nwdyads it characterized a triad by the number of 1) mutual dyads, 2) asymmetric dyads and 3) null dyads. For example, MAN = 102 means that there is one mutual dyad and two null dyads.

plot draws a bar chart of the 16 category counts, in the same fixed MAN order the text table above already uses (not sorted by count), via this package’s own established preserve/rebuild-a-plotting-dataset/restore convention - the same one nwcug’s own plot option uses for its null-distribution histogram. Grayscale by design, matching every other plot this package produces.

Examples

. nwwebuse glasgow, nwclear

. nwtriads glasgow3

    Triad census:  glasgow3

       003 |       012 |      021D |      021U |
-----------+-----------+-----------+-----------+
     16086 |      1401 |         4 |         8 |

      021C |      030T |      030C |       102 |
-----------+-----------+-----------+-----------+
         7 |         1 |         0 |      1969 |

      120D |      120U |      120C |      111D |
-----------+-----------+-----------+-----------+
         3 |        28 |        33 |         4 |

      111U |       201 |       210 |       300 |
-----------+-----------+-----------+-----------+
         1 |        17 |        26 |        12 |

     Transitivity: .4830508474576271

This example shows, e.g. that in the glasgow3 network, there are 12 triads where all nodes i, j and k are directely connected with each other.

Supported network types

Binary: yes. Directed: yes - this is the command’s native case; the full 16-type MAN classification requires a genuine directed/asymmetric-dyad distinction. Undirected: the command still runs, but 12 of the 16 categories (everything except _003/_102/_201/_300) are not meaningful for undirected data and reliably return 0, since an undirected network has no asymmetric ties by construction - nwtriads prints a note to this effect when called on an undirected network. Weighted: not applicable (a triad census is inherently a binary/dichotomous count). Signed: not checked. Two-mode: same as for the bipartite graph read as a one-mode network (valid; no mode-specific normalisation); the census counts the triples of the bipartite graph (igraph::triad_census); it has no triangle, so the transitivity is 0; closure in a two-mode network is nwclustering (its default on a two-mode network).

See also

• nwdyads

• last certified : 24 Aug 2026

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nwcommands version 3.17.6, 9 November 2026 (check your installed version)