motif_node() R function from [manynet]

Motifs at the nodal level

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)

Arguments

.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

Tetrad census

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)).

Examples


task_eg <- to_named(to_uniplex(ison_algebra, "tasks"))
(tie_cen <- node_by_tie(task_eg))
node_by_dyad(ison_networkers)
(triad_cen <- node_by_triad(task_eg))
node_by_tetrad(ison_southern_women)
node_by_path(ison_adolescents)
node_by_path(ison_southern_women)

References

On the dyad census

Holland, Paul W., and Samuel Leinhardt. 1970. "A Method for Detecting Structure in Sociometric Data". American Journal of Sociology, 76: 492-513. tools:::Rd_expr_doi("10.1016/B978-0-12-442450-0.50028-6")

On the triad census

Davis, James A., and Samuel Leinhardt. 1967. “The Structure of Positive Interpersonal Relations in Small Groups.” 55.

On the tetrad census

Ortmann, Mark, and Ulrik Brandes. 2017. “Efficient Orbit-Aware Triad and Quad Census in Directed and Undirected Graphs.” Applied Network Science 2(1):13. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1177/0190272520944151")

On paths

Dijkstra, Edsger W. 1959. "A note on two problems in connexion with graphs". Numerische Mathematik 1, 269-71. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1016/j.socnet.2010.03.006") .

motif_node function