These functions include ways to take a census of the positions of nodes in a network:
node_by_tie() returns a census of the ties in a network.
For directed networks, out-ties and in-ties are bound together.
For multiplex networks, the various types of ties are bound together.
node_by_triad() returns a census of the triad configurations
nodes are embedded in.
node_by_tetrad() returns a census of nodes' positions
in motifs of four nodes.
node_by_path() returns the shortest path lengths
of each node to every other node in the network.
node_by_tie(.data)
node_by_dyad(.data)
node_by_triad(.data)
node_by_tetrad(.data)
node_by_path(.data)The nodal tetrad census counts the number of four-node configurations that each node is embedded in. 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(node_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
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
Dijkstra, Edsger W. 1959. "A note on two problems in connexion with graphs". Numerische Mathematik 1, 269-71. doi:10.1007/BF01386390 .
Opsahl, Tore, Filip Agneessens, and John Skvoretz. 2010. "Node centrality in weighted networks: Generalizing degree and shortest paths". Social Networks 32(3): 245-51. doi:10.1016/j.socnet.2010.03.006 .
Other motifs:
motif_brokerage,
motif_diffusion,
motif_net
task_eg <- to_named(to_uniplex(ison_algebra, "tasks"))
(tie_cen <- node_by_tie(task_eg))
#> # A tibble: 16 × 33
#> names fromAutumn fromBarbara fromCarolyn fromDixie fromEstella fromFred
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Autumn 0 0 0 0 0.3 0
#> 2 Barbara 0 0 0 0 0 0
#> 3 Carolyn 0 0 0 0 0.15 0.75
#> 4 Dixie 0 0 0 0 0 0
#> 5 Estella 0.3 0 0.15 0 0 0.45
#> 6 Fred 0 0 0.6 0 0.75 0
#> # ℹ 10 more rows
#> # ℹ 26 more variables: fromGordon <dbl>, fromHobart <dbl>, fromIsaiah <dbl>,
#> # fromJosie <dbl>, fromKatie <dbl>, fromLouise <dbl>, fromMatteo <dbl>,
#> # fromNellie <dbl>, fromOtis <dbl>, fromPaisley <dbl>, toAutumn <dbl>,
#> # toBarbara <dbl>, toCarolyn <dbl>, toDixie <dbl>, toEstella <dbl>,
#> # toFred <dbl>, toGordon <dbl>, toHobart <dbl>, toIsaiah <dbl>,
#> # toJosie <dbl>, toKatie <dbl>, toLouise <dbl>, toMatteo <dbl>, …
node_by_dyad(ison_networkers)
#> # A tibble: 32 × 4
#> names Mutual Asymmetric Null
#> <chr> <dbl> <dbl> <dbl>
#> 1 Lin Freeman 29 2 1
#> 2 Doug White 21 10 1
#> 3 Ev Rogers 3 8 21
#> 4 Richard Alba 17 2 13
#> 5 Phipps Arabie 8 20 4
#> 6 Carol Barner-Barry 12 4 16
#> # ℹ 26 more rows
(triad_cen <- node_by_triad(task_eg))
#> # A tibble: 16 × 17
#> names X003 X012 X102 X021D X021U X021C X111D X111U X030T X030C X201 X120D
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Autumn 23 11 39 0 0 0 2 2 0 0 17 0
#> 2 Barba… 21 6 47 0 0 0 5 6 0 0 10 0
#> 3 Carol… 34 3 46 0 0 0 2 1 0 0 13 0
#> 4 Dixie 52 6 28 0 0 0 0 0 0 0 18 0
#> 5 Estel… 17 11 37 1 0 1 6 7 0 0 15 1
#> 6 Fred 23 8 40 1 0 0 3 3 0 0 18 1
#> # ℹ 10 more rows
#> # ℹ 4 more variables: X120U <dbl>, X120C <dbl>, X210 <dbl>, X300 <dbl>
node_by_tetrad(ison_southern_women)
#> # A tibble: 18 × 12
#> names E4 I4 H4 L4 D4 U4 Y4 P4 C4 Z4 X4
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Evelyn 1241 1347 176 1138 272 0 246 0 75 0 0
#> 2 Laura 1365 1389 180 1077 213 0 203 0 68 0 0
#> 3 Theresa 1333 1244 123 1137 286 0 281 0 91 0 0
#> 4 Brenda 1384 1356 176 1093 210 0 205 0 71 0 0
#> 5 Charlotte 1728 1562 157 836 117 0 74 0 21 0 0
#> 6 Frances 1840 1433 114 810 134 0 134 0 30 0 0
#> # ℹ 12 more rows
#> # A tibble: 14 × 12
#> names E4 I4 H4 L4 D4 U4 Y4 P4 C4 Z4 X4
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 E1 1877 1632 96 710 113 0 52 0 15 0 0
#> 2 E2 1886 1631 84 698 122 0 58 0 16 0 0
#> 3 E3 1368 1611 190 1006 168 0 98 0 54 0 0
#> 4 E4 1681 1673 131 784 138 0 64 0 24 0 0
#> 5 E5 1061 1557 232 1208 216 0 140 0 81 0 0
#> 6 E6 1085 1576 178 1142 287 0 156 0 71 0 0
#> # ℹ 8 more rows
node_by_path(ison_adolescents)
#> # A tibble: 8 × 9
#> names Betty Sue Alice Jane Dale Pam Carol Tina
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Betty 0 1 2 3 2 2 3 4
#> 2 Sue 1 0 1 2 1 1 2 3
#> 3 Alice 2 1 0 1 1 1 2 3
#> 4 Jane 3 2 1 0 1 2 3 4
#> 5 Dale 2 1 1 1 0 2 3 4
#> 6 Pam 2 1 1 2 2 0 1 2
#> # ℹ 2 more rows
node_by_path(ison_southern_women)
#> # A tibble: 18 × 33
#> names Evelyn Laura Theresa Brenda Charlotte Frances Eleanor Pearl Ruth Verne
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Evelyn 0 2 2 2 2 2 2 2 2 2
#> 2 Laura 2 0 2 2 2 2 2 2 2 2
#> 3 There… 2 2 0 2 2 2 2 2 2 2
#> 4 Brenda 2 2 2 0 2 2 2 2 2 2
#> 5 Charl… 2 2 2 2 0 2 2 4 2 2
#> 6 Franc… 2 2 2 2 2 0 2 2 2 2
#> # ℹ 12 more rows
#> # ℹ 22 more variables: Myra <dbl>, Katherine <dbl>, Sylvia <dbl>, Nora <dbl>,
#> # Helen <dbl>, Dorothy <dbl>, Olivia <dbl>, Flora <dbl>, E1 <dbl>, E2 <dbl>,
#> # E3 <dbl>, E4 <dbl>, E5 <dbl>, E6 <dbl>, E7 <dbl>, E8 <dbl>, E9 <dbl>,
#> # E10 <dbl>, E11 <dbl>, E12 <dbl>, E13 <dbl>, E14 <dbl>
#> # A tibble: 14 × 33
#> names Evelyn Laura Theresa Brenda Charlotte Frances Eleanor Pearl Ruth Verne
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 E1 1 1 3 1 3 3 3 3 3 3
#> 2 E2 1 1 1 3 3 3 3 3 3 3
#> 3 E3 1 1 1 1 1 1 3 3 3 3
#> 4 E4 1 3 1 1 1 3 3 3 3 3
#> 5 E5 1 1 1 1 1 1 1 3 1 3
#> 6 E6 1 1 1 1 3 1 1 1 3 3
#> # ℹ 8 more rows
#> # ℹ 22 more variables: Myra <dbl>, Katherine <dbl>, Sylvia <dbl>, Nora <dbl>,
#> # Helen <dbl>, Dorothy <dbl>, Olivia <dbl>, Flora <dbl>, E1 <dbl>, E2 <dbl>,
#> # E3 <dbl>, E4 <dbl>, E5 <dbl>, E6 <dbl>, E7 <dbl>, E8 <dbl>, E9 <dbl>,
#> # E10 <dbl>, E11 <dbl>, E12 <dbl>, E13 <dbl>, E14 <dbl>