motif_node: Motifs at the nodal level

In manynet: Many Ways to Make, Modify, Map, Mark, and Measure Myriad Networks

Motifs at the nodal level

Description

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.

Usage

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)).

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.socnet.2010.03.006")}.

See Also

Other motifs: motif_brokerage, motif_diffusion, motif_net

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)

manynet documentation built on June 23, 2025, 9:07 a.m.