Considering the triad census of Davis and Leinhardt (1972) for vector A, B, and C:
Arguments
- A
A symmetric matrix object
- ztest
Return Z and p-value
- covar
Return the covarianc matrix for triadic analysis
Value
This function gives the counts of the triad census, the expected counts, assuming that U|MAN distribution (Holland and Leinhardt, 1975, 1976) is operating, and the standard deviations of these counts.
Details
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.
References
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.
Holland, P. W. and Leinhardt, S. (1975). The statistical analysis of local structure in social networks. In D. R. Heise (Ed.), Sociological Methodology, 1976 (Jossey-Bass, pp. 1–45).
Holland, P. W. and Leinhardt, S. (1976). Local Structure in Social Networks. Sociological Methodology, 7, 1–45. doi: https://doi.org/10.2307/270703
Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.
Examples
data(krackhardt_friends)
triad_uman(krackhardt_friends)
#> label OBS EXP VAR STD
#> 1 003 376 320.057 88.239 9.394
#> 2 012 366 416.818 211.856 14.555
#> 3 102 143 171.193 88.921 9.430
#> 4 021D 114 44.087 38.736 6.224
#> 5 021U 34 44.087 38.736 6.224
#> 6 021C 35 88.173 66.770 8.171
#> 7 111D 39 73.745 60.470 7.776
#> 8 111U 101 73.745 60.470 7.776
#> 9 030T 23 18.173 14.902 3.860
#> 10 030C 0 6.058 5.694 2.386
#> 11 201 20 28.971 20.471 4.524
#> 12 120D 16 7.740 7.359 2.713
#> 13 120U 25 7.740 7.359 2.713
#> 14 120C 9 15.481 13.957 3.736
#> 15 210 23 12.385 10.534 3.246
#> 16 300 6 1.548 1.441 1.200
if (FALSE) {
triad_uman(krackhardt_friends, ztest = TRUE, covar = TRUE)
}