motif_node {manynet}

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_quad() 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_triad(.data)

node_by_quad(.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

Quad census

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.

References

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.

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))
(triad_cen <- node_by_triad(task_eg))
node_by_quad(manynet::ison_southern_women)
node_by_path(manynet::ison_adolescents)
node_by_path(manynet::ison_southern_women)