I am analyzing an undirected graph in R. I'm trying to (eventually) write a function to get the ratio of the size (number of vertices) of the largest connected component to the size of the largest biconnected component - of any random graph. I was able to extract the size of the largest connected component, but am having trouble with the size of the largest biconnected component. I started off using the igraph function biconnected_components on graph g:
bicomponent_list <- biconnected_components(g)
bicomponent_list$components # lists all of the components, including size and vertex names
length(bicomponent_list$components[[1]]) # returns number of vertices of first bicomponent
Then my half-baked idea was to somehow order this list in decreasing number of vertices, so that I can always call length(bicomponent_list$components[[1]]) and it will be the largest biconnected component. But I don't know how to sort this correctly. Perhaps I have to convert it to a vector? But I also don't know how to specify that I want the number of vertices in the vector. Does anyone know, or have a better way to do it? Thanks so much!
library(igraph)
# generating sample graph
g1 <- barabasi.game(100, 1, 5)
V(g1)$name <- as.character(1:100)
g2 <- erdos.renyi.game(50, graph.density(g1), directed = TRUE)
V(g2)$name <- as.character(101:200)
g3 <- graph.union(g1, g2, byname = TRUE)
# analyzing the bicomponents
bicomponent_list <- biconnected_components(g3)
bi_list <- as.list(bicomponent_list$components)
bi_list <- lapply(bi_list, length) # lists the sizes of all of the components that I want to reorder
My desired outcome would be ordering
bi_list
such thatlength(bicomponent_list$components[[1]])
returns the bicomponent with the most vertices.