Use this if you are using igraph from R
A vertex set is called independent if there no edges between any two vertices in it. These functions find independent vertex sets in undirected graphs
ivs(graph, min = NULL, max = NULL)
graph |
The input graph, directed graphs are considered as undirected, loop edges and multiple edges are ignored. |
min |
Numeric constant, limit for the minimum size of the independent
vertex sets to find. |
max |
Numeric constant, limit for the maximum size of the independent
vertex sets to find. |
ivs
finds all independent vertex sets in the
network, obeying the size limitations given in the min
and max
arguments.
largest_ivs
finds the largest independent vertex
sets in the graph. An independent vertex set is largest if there is no
independent vertex set with more vertices.
maximal_ivs
finds the maximal independent vertex
sets in the graph. An independent vertex set is maximal if it cannot be
extended to a larger independent vertex set. The largest independent vertex
sets are maximal, but the opposite is not always true.
independece.number
calculate the size of the largest independent
vertex set(s).
These functions use the algorithm described by Tsukiyama et al., see reference below.
ivs
,
largest_ivs
and
maximal_ivs
return a list containing numeric
vertex ids, each list element is an independent vertex set.
ivs_size
returns an integer constant.
Tamas Nepusz ntamas@gmail.com ported it from the Very Nauty Graph Library by Keith Briggs (http://keithbriggs.info/) and Gabor Csardi csardi.gabor@gmail.com wrote the R interface and this manual page.
S. Tsukiyama, M. Ide, H. Ariyoshi and I. Shirawaka. A new algorithm for generating all the maximal independent sets. SIAM J Computing, 6:505–517, 1977.
# Do not run, takes a couple of seconds ## Not run: # A quite dense graph set.seed(42) g <- sample_gnp(100, 0.9) ivs_size(g) ivs(g, min=ivs_size(g)) largest_ivs(g) # Empty graph induced_subgraph(g, largest_ivs(g)[[1]]) length(maximal_ivs(g)) ## End(Not run)