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A bipartite graph is projected into two one-mode networks


  types = NULL,
  multiplicity = TRUE,
  probe1 = NULL,
  which = c("both", "true", "false"),
  remove.type = TRUE

bipartite_projection_size(graph, types = NULL)



The input graph. It can be directed, but edge directions are ignored during the computation.


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.


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.


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.


A character scalar to specify which projection(s) to calculate. The default is to calculate both.


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.


A list of two undirected graphs. See details above.


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


Gabor Csardi


## 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)
#>       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 eda2d12 UNW- 5 6 -- Event network
#> + attr: name (g/c), name (v/c), weight (e/n)
#> + edges from eda2d12 (vertex names):
#> [1] Alice--Bob   Alice--Cecil Alice--Dan   Bob  --Cecil Bob  --Dan  
#> [6] Cecil--Dan  
print(proj2[[2]], g = TRUE, e = TRUE)
#> IGRAPH 9c40952 UNW- 3 2 -- Event network
#> + attr: name (g/c), name (v/c), weight (e/n)
#> + edges from 9c40952 (vertex names):
#> [1] Party --Skiing    Skiing--Badminton