A bipartite graph is projected into two one-mode networks
Usage
bipartite_projection(
graph,
types = NULL,
multiplicity = TRUE,
probe1 = NULL,
which = c("both", "true", "false"),
remove.type = TRUE
)
bipartite_projection_size(graph, types = NULL)
Arguments
- graph
The input graph. It can be directed, but edge directions are ignored during the computation.
- types
An optional vertex type vector to use instead of the ‘
type
’ vertex attribute. You must supply this argument if the graph has no ‘type
’ vertex attribute.- multiplicity
If
TRUE
, then igraph keeps the multiplicity of the edges as an edge attribute called ‘weight’. E.g. if there is an A-C-B and also an A-D-B triple in the bipartite graph (but no more X, such that A-X-B is also in the graph), then the multiplicity of the A-B edge in the projection will be 2.- probe1
This argument can be used to specify the order of the projections in the resulting list. If given, then it is considered as a vertex id (or a symbolic vertex name); the projection containing this vertex will be the first one in the result list. This argument is ignored if only one projection is requested in argument
which
.- which
A character scalar to specify which projection(s) to calculate. The default is to calculate both.
- remove.type
Logical scalar, whether to remove the
type
vertex attribute from the projections. This makes sense because these graphs are not bipartite any more. However if you want to combine them with each other (or other bipartite graphs), then it is worth keeping this attribute. By default it will be removed.
Details
Bipartite graphs have a type
vertex attribute in igraph, this is
boolean and FALSE
for the vertices of the first kind and TRUE
for vertices of the second kind.
bipartite_projection_size()
calculates the number of vertices and edges
in the two projections of the bipartite graphs, without calculating the
projections themselves. This is useful to check how much memory the
projections would need if you have a large bipartite graph.
bipartite_projection()
calculates the actual projections. You can use
the probe1
argument to specify the order of the projections in the
result. By default vertex type FALSE
is the first and TRUE
is
the second.
bipartite_projection()
keeps vertex attributes.
See also
Bipartite graphs
bipartite_mapping()
,
is_bipartite()
Author
Gabor Csardi csardi.gabor@gmail.com
Examples
## Projection of a full bipartite graph is a full graph
g <- make_full_bipartite_graph(10, 5)
proj <- bipartite_projection(g)
graph.isomorphic(proj[[1]], make_full_graph(10))
#> [1] TRUE
graph.isomorphic(proj[[2]], make_full_graph(5))
#> [1] TRUE
## The projection keeps the vertex attributes
M <- matrix(0, nrow = 5, ncol = 3)
rownames(M) <- c("Alice", "Bob", "Cecil", "Dan", "Ethel")
colnames(M) <- c("Party", "Skiing", "Badminton")
M[] <- sample(0:1, length(M), replace = TRUE)
M
#> Party Skiing Badminton
#> Alice 1 1 0
#> Bob 0 1 0
#> Cecil 0 1 0
#> Dan 0 1 1
#> Ethel 0 0 0
g2 <- graph_from_biadjacency_matrix(M)
g2$name <- "Event network"
proj2 <- bipartite_projection(g2)
print(proj2[[1]], g = TRUE, e = TRUE)
#> IGRAPH 567e6ba UNW- 5 6 -- Event network
#> + attr: name (g/c), name (v/c), weight (e/n)
#> + edges from 567e6ba (vertex names):
#> [1] Alice--Bob Alice--Cecil Alice--Dan Bob --Cecil Bob --Dan
#> [6] Cecil--Dan
print(proj2[[2]], g = TRUE, e = TRUE)
#> IGRAPH 795b6e7 UNW- 3 2 -- Event network
#> + attr: name (g/c), name (v/c), weight (e/n)
#> + edges from 795b6e7 (vertex names):
#> [1] Party --Skiing Skiing--Badminton