node_census  R Documentation 
These functions include ways to take a census of the positions of nodes in a network:
node_tie_census()
returns a census of the ties in a network.
For directed networks, outties and inties are bound together.
for multiplex networks, the various types of 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.
node_tie_census(.data)
node_triad_census(.data)
node_quad_census(.data)
node_path_census(.data)
.data 
An object of a

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 censuslabelling practices.
The letternumber pairing of these labels indicate
the number and configuration of ties.
For now, we offer a rough translation:
migraph  Ortmann and Brandes 
E4  coK4 
I40, I41  codiamond 
H4  coC4 
L42, L41, L40  copaw 
D42, D40  coclaw 
U42, U41  P4 
Y43, Y41  claw 
P43, P42, P41  paw 
04  C4 
Z42, Z43  diamond 
X4  K4 
See also this list of graph classes.
Davis, James A., and Samuel Leinhardt. 1967. “The Structure of Positive Interpersonal Relations in Small Groups.” 55.
Ortmann, Mark, and Ulrik Brandes. 2017. “Efficient OrbitAware Triad and Quad Census in Directed and Undirected Graphs.” Applied Network Science 2(1):13. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s4110901700272")}.
Dijkstra, Edsger W. 1959. "A note on two problems in connexion with graphs". Numerische Mathematik 1, 26971. \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): 24551. \Sexpr[results=rd]{tools:::Rd_expr_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, "tasks"))
(tie_cen < node_tie_census(task_eg))
(triad_cen < node_triad_census(task_eg))
node_quad_census(manynet::ison_southern_women)
node_path_census(manynet::ison_adolescents)
node_path_census(manynet::ison_southern_women)
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