This function explores dyads and triads (Simmel, 1950), building from the 'forbidden triad' (Granovetter, 1973). First, the minimum structure is an isolated node, then dyads. Afterwards, different combinations of 'forbidden triads' are explored.
Arguments
- A
A symmetric matrix object.
- adjacency_list
Whether to return the adjacency list of the triads per node.
- min
Numeric constant, lower limit on the number of forbidden triads (201) of which a node is the centre. NULL means no limit.
- max
Numeric constant, upper limit on the number of forbidden triads (201) of which a node is the centre. NULL means no limit.
Value
This function returns a data frame with the triads of each node: the node, the number of the
triad, its members and its type.
If adjacency_list = TRUE it also return the adjacency list of
the triads per node.
Details
For each node, every pair of its neighbours forms a triad with the node at its centre. The triad is a
forbidden triad (type 201) when the two neighbours are not tied, which Granovetter (1973) argued is
unlikely when both ties are strong, and it is closed (type 300) when they are. A node with a single
neighbour is listed with its dyad (type 102) and an isolated node alone (type 003). The
underlying graph of the network is used.
The same triad receives the same number in triad for every node that lists it: a closed triad is
listed by its three nodes, and a forbidden triad only by its centre.
References
Granovetter, M.S. (1973). The Strength of Weak Ties. American Journal of Sociology. 78 (6): 1360–80. doi:10.1086/225469 .
Simmel, G. (1950). Individual and Society. In K. H. Wolff (Ed.), The Sociology of George Simmel. New York: Free Press.
Wasserman, S. and Faust, K. (1994). Social network analysis: Methods and applications. Cambridge University Press.
Examples
A <- matrix(c(
0, 1, 1, 1, 0,
1, 0, 1, 0, 0,
1, 1, 0, 0, 0,
1, 0, 0, 0, 1,
0, 0, 0, 1, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- letters[1:ncol(A)]
dyad_triad_table(A)
#> node triad members type
#> 1 a 1 a|b|c 300
#> 2 a 2 a|b|d 201
#> 3 a 3 a|c|d 201
#> 4 b 1 a|b|c 300
#> 5 c 1 a|b|c 300
#> 6 d 4 a|d|e 201
#> 7 e 5 d|e 102
# Nodes at the centre of at least two forbidden triads
dyad_triad_table(A, adjacency_list = TRUE, min = 2)
#> $nodes
#> node triad members type
#> 1 a 1 a|b|c 300
#> 2 a 2 a|b|d 201
#> 3 a 3 a|c|d 201
#>
#> $adjacency_list
#> $adjacency_list$a
#> [1] "a|b|c" "a|b|d" "a|c|d"
#>
#>