These functions include ways to take a census of the positions of nodes in a network. These include a triad census based on the triad profile of nodes, but also a tie census based on the particular tie partners of nodes. Included also are group census functions for summarising the profiles of clusters of nodes in a network.
node_tie_census(.data)
node_triad_census(.data)
node_quad_census(.data)
node_path_census(.data)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
The quad census uses the {oaqc} package to do
the heavy lifting of counting the number of each orbits.
See vignette('oaqc').
However, our function relabels some of the motifs
to avoid conflicts and improve some consistency with
other census-labelling practices.
The letter-number pairing of these labels indicate
the number and configuration of ties.
For now, we offer a rough translation:
| migraph | Ortmann and Brandes |
| E4 | co-K4 |
| I40, I41 | co-diamond |
| H4 | co-C4 |
| L42, L41, L40 | co-paw |
| D42, D40 | co-claw |
| U42, U41 | P4 |
| Y43, Y41 | claw |
| P43, P42, P41 | paw |
| 04 | C4 |
| Z42, Z43 | diamond |
| X4 | K4 |
See also this list of graph classes.
node_tie_census(): Returns a census of the ties in a network.
For directed networks, out-ties and in-ties are bound together.
node_triad_census(): Returns a census of the triad configurations
nodes are embedded in.
node_quad_census(): Returns a census of nodes' positions
in motifs of four nodes.
node_path_census(): Returns the shortest path lengths
of each node to every other node in the network.
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 .
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:
brokerage_census,
network_census
task_eg <- manynet::to_named(manynet::to_uniplex(manynet::ison_algebra, "task_tie"))
(tie_cen <- node_tie_census(task_eg))
#> # A tibble: 16 × 33
#> names fromJose fromGeraldine fromMarissa fromColton fromHeidi fromChristopher
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Jose 0 1 0 0 1 1
#> 2 Gera… 0 0 1 0 0 0
#> 3 Mari… 0 1 0 0 1 1
#> 4 Colt… 0 0 0 0 0 0
#> 5 Heidi 1 0 1 0 0 1
#> 6 Chri… 0 0 1 0 1 0
#> 7 Flos… 0 1 1 0 0 1
#> 8 Rosa 1 1 1 0 1 1
#> 9 Etta 1 0 0 0 0 0
#> 10 Mere… 1 0 1 1 1 1
#> 11 Darl… 1 0 1 0 1 1
#> 12 Cole 1 1 0 0 0 1
#> 13 Alexa 1 1 0 0 1 0
#> 14 Micah 0 1 1 0 0 1
#> 15 Xand… 1 1 1 0 1 0
#> 16 Alice 1 1 1 1 1 1
#> # ℹ 26 more variables: fromFlossie <dbl>, fromRosa <dbl>, fromEtta <dbl>,
#> # fromMeredith <dbl>, fromDarlene <dbl>, fromCole <dbl>, fromAlexa <dbl>,
#> # fromMicah <dbl>, fromXander <dbl>, fromAlice <dbl>, toJose <dbl>,
#> # toGeraldine <dbl>, toMarissa <dbl>, toColton <dbl>, toHeidi <dbl>,
#> # toChristopher <dbl>, toFlossie <dbl>, toRosa <dbl>, toEtta <dbl>,
#> # toMeredith <dbl>, toDarlene <dbl>, toCole <dbl>, toAlexa <dbl>,
#> # toMicah <dbl>, toXander <dbl>, toAlice <dbl>
(triad_cen <- node_triad_census(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 Jose 6 12 32 0 1 0 7 3 0 0 8 1
#> 2 Gera… 15 12 42 0 0 0 0 5 0 0 4 1
#> 3 Mari… 20 5 37 0 0 0 3 3 0 0 12 0
#> 4 Colt… 102 0 3 0 0 0 0 0 0 0 0 0
#> 5 Heidi 15 5 41 0 0 0 2 1 0 0 13 0
#> 6 Chri… 20 5 41 0 0 0 3 2 0 0 11 0
#> 7 Flos… 28 0 51 0 0 0 0 2 0 0 6 0
#> 8 Rosa 18 0 42 0 0 0 2 1 0 0 18 0
#> 9 Etta 86 2 17 0 0 0 0 0 0 0 0 0
#> 10 Mere… 25 6 35 0 0 0 3 3 0 0 15 0
#> 11 Darl… 65 4 36 0 0 0 0 0 0 0 0 0
#> 12 Cole 72 3 30 0 0 0 0 0 0 0 0 0
#> 13 Alexa 76 3 26 0 0 0 0 0 0 0 0 0
#> 14 Micah 56 2 47 0 0 0 0 0 0 0 0 0
#> 15 Xand… 58 5 42 0 0 0 0 0 0 0 0 0
#> 16 Alice 0 0 0 0 0 0 0 0 0 0 44 0
#> # ℹ 4 more variables: X120U <dbl>, X120C <dbl>, X210 <dbl>, X300 <dbl>
node_quad_census(manynet::ison_southern_women)
#> # A tibble: 32 × 13
#> names E4 I41 I40 H4 L42 L41 L40 U42 U41 Y43 Y41 X04
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 EVEL… 1402 1046 474 202 397 692 148 200 78 56 190 75
#> 2 LAURA 1539 986 579 202 323 659 182 134 85 35 168 68
#> 3 THER… 1499 975 434 147 364 784 91 217 77 56 225 91
#> 4 BREN… 1559 968 562 198 320 682 179 134 82 35 170 71
#> 5 CHAR… 1945 763 972 171 117 419 359 30 89 4 70 21
#> 6 FRAN… 2063 652 944 126 102 502 269 36 102 4 130 30
#> 7 ELEA… 2122 598 930 98 93 546 224 42 114 4 156 33
#> 8 PEARL 2313 439 1089 65 42 448 252 28 112 1 154 17
#> 9 RUTH 2180 549 918 73 80 577 178 56 123 4 190 32
#> 10 VERNE 2166 561 920 82 83 567 190 53 118 4 184 32
#> # ℹ 22 more rows
node_path_census(manynet::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
#> 7 Carol 3 2 2 3 3 1 0 1
#> 8 Tina 4 3 3 4 4 2 1 0
node_path_census(manynet::ison_southern_women)
#> # A tibble: 32 × 33
#> names EVELYN LAURA THERESA BRENDA CHARLOTTE FRANCES ELEANOR PEARL RUTH VERNE
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 EVEL… 0 2 2 2 2 2 2 2 2 2
#> 2 LAURA 2 0 2 2 2 2 2 2 2 2
#> 3 THER… 2 2 0 2 2 2 2 2 2 2
#> 4 BREN… 2 2 2 0 2 2 2 2 2 2
#> 5 CHAR… 2 2 2 2 0 2 2 4 2 2
#> 6 FRAN… 2 2 2 2 2 0 2 2 2 2
#> 7 ELEA… 2 2 2 2 2 2 0 2 2 2
#> 8 PEARL 2 2 2 2 4 2 2 0 2 2
#> 9 RUTH 2 2 2 2 2 2 2 2 0 2
#> 10 VERNE 2 2 2 2 2 2 2 2 2 0
#> # ℹ 22 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>