node_x_clique() returns which maximal cliques each node belongs to.
A clique is a set of nodes every one of which is tied to every other,
and it is maximal if no further node can be added without breaking that.
Cliques are the strictest notion of a cohesive subgroup,
and unlike the communities returned by node_in_*() functions they
overlap: a node may belong to many cliques at once, or to none.
That is why this returns an incidence table rather than a membership
vector.
node_x_percolation() returns which communities of adjacent cliques
each node belongs to, by clique percolation.
These communities also overlap, but there are fewer of them than there
are cliques, since cliques that share most of their nodes are joined.
node_x_clique(.data, min_clique_size = 3)
node_x_percolation(.data, min_clique_size = 3)A network object of class stocnet, igraph, tbl_graph, network, or similar.
Internally any of these will be coerced to an efficient implementation.
For more information on possible coercions, see e.g. manynet::as_stocnet().
Integer, the minimum size of clique to return.
By default 3, since dyads and isolates are trivially cliques.
For a two-mode network, a vector of two values giving the minimum number
of nodes from each mode, by default c(3, 3).
A node_motif matrix with one row for each node in the network and
a column for each motif type,
giving the count of each motif in which each node participates.
It is printed as a tibble, however, to avoid greedy printing.
If the network is labelled,
then the node names will be in a column named names.
For signed networks, only the positive ties are considered.
Since a clique is a maximally cohesive subgroup, negative ties cannot
contribute to one.
Use manynet::to_unsigned() first to control this yourself.
In a two-mode network no two nodes of the same mode are ever tied
directly, so no set of them is a clique in the ordinary sense.
The two-mode analogue is a biclique: a set of nodes from each mode such
that every node of the one is tied to every node of the other.
node_x_clique() detects these by connecting nodes that share a partner
before searching, so that a biclique becomes an ordinary clique,
and then keeping only those cliques with at least min_clique_size nodes
from each mode.
Clique percolation (Palla et al. 2005) treats two cliques as adjacent
where they share all but one of min_clique_size nodes,
so with the default of 3 where they share a tie.
A community is then a set of cliques that can be reached from each other
through such adjacent cliques,
and a node belongs to every community that holds a clique it is in.
A node in no clique of at least min_clique_size belongs to none.
Luce, R. Duncan, and Albert D. Perry. 1949. "A method of matrix analysis of group structure". Psychometrika 14(2): 95-116. doi:10.1007/BF02289146
Palla, Gergely, Imre Derényi, Illés Farkas, and Tamás Vicsek. 2005. "Uncovering the overlapping community structure of complex networks in nature and society". Nature 435(7043): 814-818. doi:10.1038/nature03607
Other motifs:
motif_accuracy_node,
motif_brokerage_net,
motif_brokerage_node,
motif_composition,
motif_exposure,
motif_hazard,
motif_hierarchy,
motif_homophily,
motif_net,
motif_node,
motif_path,
motif_periods
Other nodal:
mark_core,
mark_degree,
mark_diff,
mark_nodes,
mark_select_node,
measure_accuracy_node,
measure_assort_node,
measure_broker_node,
measure_brokerage,
measure_central_between,
measure_central_close,
measure_central_degree,
measure_central_eigen,
measure_closure_node,
measure_core,
measure_diffusion_node,
measure_diverse_node,
member_brokerage,
member_cliques,
member_community,
member_community_hier,
member_community_modular,
member_community_partition,
member_community_spread,
member_components,
member_core,
member_diffusion,
member_equivalence,
motif_accuracy_node,
motif_brokerage_node,
motif_composition,
motif_exposure,
motif_node,
motif_path
node_x_clique(ison_adolescents)
#> # A tibble: 8 × 4
#> names C1 C2 C3
#> <chr> <int> <int> <int>
#> 1 Betty 0 0 0
#> 2 Sue 0 1 1
#> 3 Alice 1 1 1
#> 4 Jane 1 0 0
#> 5 Dale 1 1 0
#> 6 Pam 0 0 1
#> # ℹ 2 more rows
node_x_clique(ison_southern_women, min_clique_size = c(3, 3))
#> # A tibble: 18 × 23
#> names C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12
#> <chr> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
#> 1 Evelyn 1 0 0 0 0 0 0 0 0 1 0 1
#> 2 Laura 1 0 0 0 0 0 0 0 0 0 0 0
#> 3 There… 1 0 0 0 0 0 0 0 0 1 1 1
#> 4 Brenda 0 0 0 0 0 0 0 0 0 1 1 1
#> 5 Charl… 0 0 0 0 0 0 0 0 0 1 1 0
#> 6 Franc… 0 0 0 0 0 0 0 0 0 0 0 0
#> # ℹ 12 more rows
#> # ℹ 10 more variables: C13 <int>, C14 <int>, C15 <int>, C16 <int>, C17 <int>,
#> # C18 <int>, C19 <int>, C20 <int>, C21 <int>, C22 <int>
#> # A tibble: 14 × 23
#> names C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12
#> <chr> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int> <int>
#> 1 E1 0 0 0 0 0 0 0 0 0 0 0 0
#> 2 E2 1 0 0 0 0 0 0 0 0 0 0 0
#> 3 E3 1 0 0 0 0 0 0 0 0 1 1 1
#> 4 E4 0 0 0 0 0 0 0 0 0 1 1 1
#> 5 E5 1 0 0 0 0 0 0 0 0 1 1 1
#> 6 E6 1 0 0 0 0 0 0 0 0 0 0 1
#> # ℹ 8 more rows
#> # ℹ 10 more variables: C13 <int>, C14 <int>, C15 <int>, C16 <int>, C17 <int>,
#> # C18 <int>, C19 <int>, C20 <int>, C21 <int>, C22 <int>
node_x_percolation(ison_adolescents)
#> # A tibble: 8 × 2
#> names C1
#> <chr> <int>
#> 1 Betty 0
#> 2 Sue 1
#> 3 Alice 1
#> 4 Jane 1
#> 5 Dale 1
#> 6 Pam 1
#> # ℹ 2 more rows