Triad census was defined by David and Leinhardt (see References
below). Every triple of vertices (A, B, C) are classified into the 16
possible states:
003
{A,B,C, the empty graph.}
012{A->B, C, the graph with a single directed edge.}
102{A<->B, C, the graph with a mutual connection between two
vertices.}
021D{A<-B->C, the out-star.}
021U{A->B<-C, the 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, the complete graph.}
References
See also Davis, J.A. and Leinhardt, S. (1972). The Structure of
Positive Interpersonal Relations in Small Groups. In J. Berger
(Ed.), Sociological Theories in Progress, Volume 2, 218-251.
Boston: Houghton Mifflin.
See Also
dyad.census for classifying binary relationships,
graph.motifs for the underlying implementation.