These functions include ways to take a census of the graphlets in a network:
net_by_dyad() returns a census of dyad motifs in a network.
net_by_triad() returns a census of triad motifs in a network.
net_by_tetrad() returns a census of tetrad motifs in a network.
net_by_mixed() returns a census of triad motifs that span
a one-mode and a two-mode network.
See also graph classes.
net_by_dyad(.data)
net_by_triad(.data)
net_by_tetrad(.data)
net_by_mixed(.data, object2)Alejandro Espinosa 'netmem'
An object of a manynet-consistent class:
matrix (adjacency or incidence) from {base} R
edgelist, a data frame from {base} R or tibble from {tibble}
igraph, from the {igraph} package
network, from the {network} package
tbl_graph, from the {tidygraph} package
A second, two-mode migraph-consistent object.
The tetrad census counts the number of four-node configurations in the network. The function returns a matrix with a special naming convention:
E4 (aka co-K4): This is an empty set of four nodes; no ties
I4 (aka co-diamond): This is a set of four nodes with just one tie
H4 (aka co-C4): This set of four nodes includes two non-adjacent ties
L4 (aka co-paw): This set of four nodes includes two adjacent ties
D4 (aka co-claw): This set of four nodes includes three adjacent ties, in the form of a triangle with one isolate
U4 (aka P4, four-actor line): This set of four nodes includes three ties arranged in a line
Y4 (aka claw): This set of four nodes includes three ties all adjacent to a single node
P4 (aka paw, kite): This set of four nodes includes four ties arranged as a triangle with an extra tie hanging off of one of the nodes
C4 (aka bifan): This is a symmetric box or 4-cycle or set of shared choices
Z4 (aka diamond): This resembles C4 but with an extra tie cutting across the box
X4 (aka K4): This resembles C4 but with two extra ties cutting across the box; a realisation of all possible ties
Graphs of these motifs can be shown using
plot(net_by_tetrad(ison_southern_women)).
Holland, Paul W., and Samuel Leinhardt. 1970. "A Method for Detecting Structure in Sociometric Data". American Journal of Sociology, 76: 492-513. doi:10.1016/B978-0-12-442450-0.50028-6
Wasserman, Stanley, and Katherine Faust. 1994. "Social Network Analysis: Methods and Applications". Cambridge: Cambridge University Press.
Davis, James A., and Samuel Leinhardt. 1967. “The Structure of Positive Interpersonal Relations in Small Groups.” 55.
Ortmann, Mark, and Ulrik Brandes. 2017. “Efficient Orbit-Aware Triad and Quad Census in Directed and Undirected Graphs.” Applied Network Science 2(1):13. doi:10.1007/s41109-017-0027-2 .
McMillan, Cassie, and Diane Felmlee. 2020. "Beyond Dyads and Triads: A Comparison of Tetrads in Twenty Social Networks". Social Psychology Quarterly 83(4): 383-404. doi:10.1177/0190272520944151
Hollway, James, Alessandro Lomi, Francesca Pallotti, and Christoph Stadtfeld. 2017. “Multilevel Social Spaces: The Network Dynamics of Organizational Fields.” Network Science 5(2): 187–212. doi:10.1017/nws.2017.8
Other motifs:
motif_brokerage,
motif_diffusion,
motif_node
net_by_dyad(manynet::ison_algebra)
#> # A tibble: 1 × 3
#> Mutual Asymmetric Null
#> <dbl> <dbl> <dbl>
#> 1 68 8 44
net_by_triad(manynet::ison_adolescents)
#> # A tibble: 1 × 6
#> `003` `012` `102` `201` `210` `300`
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 13 0 29 11 0 3
net_by_tetrad(ison_southern_women)
#> # A tibble: 1 × 11
#> E4 I4 H4 L4 D4 U4 Y4 P4 C4 Z4 X4
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 12388 0 11869 0 0 0 0 0 7458 0 2758
marvel_friends <- to_unsigned(ison_marvel_relationships, "positive")
(mixed_cen <- net_by_mixed(marvel_friends, ison_marvel_teams))
#> # A tibble: 1 × 10
#> `22` `21` `20` `12` `11D` `11U` `10` `02` `01` `00`
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1137 0 1702 7064 0 0 22774 30856 0 130765