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**NETWORK > TRIAD CENSUS**

**PURPOSE **Performs a triad census of a directed network.

**DESCRIPTION **In a directed network there are sixteen possible triads. This routine counts the number of each type of triad present in a directed network. The triads are labelled abcZ where a is the number of reciprocated ties, b is the number of unreciprocated ties and c is the number of null ties. The Z term is a letter (U,C,D orT) used to differentiate between different triads in which these numbers are the same. For an undirected netork there are only 4 possible triads namely 003, 102, 201 and 300.

**PARAMETERS**

**Input network **

** **Name of file containing dataset to be analyzed. Data type: digraph.

**Output Matrix:** (Default = <inputfilename>-tri)

Name output matrix with triad counts.

**LOG FILE** Table of counts of each triad type. For each triad consisting of vertices A,B,C these are

003 = A,B,C, empty triad.

012 = A->B, C, triad with a single directed edge.

102 = A<->B, C, triad with a reciprocated connection between two vertices.

021D = A<-B->C, triadic out-star.

021U = A->B<-C triadic in-star.

021C = A->B->C, directed line.

111D = A<->B<-C.

111U = A<->B->C.

030T = A->B<-C, A->C.

030C = A<-B<-C, A->C.

201 = A<->B<->C.

120D = A<-B->C, A<->C.

120U = A->B<-C, A<->C.

120C = A->B->C, A<->C.

210 = A->B<->C, A<->C.

300 = A<->B<->C, A<->C, complete triad.

**TIMING** O(N^3)

**COMMENTS** None.

**REFERENCES** None.