Use this if you are using igraph from R
min_cut
calculates the minimum stcut between two vertices in a graph
(if the source
and target
arguments are given) or the minimum
cut of the graph (if both source
and target
are NULL
).
min_cut(graph, source = NULL, target = NULL, capacity = NULL, value.only = TRUE)
graph 
The input graph. 
source 
The id of the source vertex. 
target 
The id of the target vertex (sometimes also called sink). 
capacity 
Vector giving the capacity of the edges. If this is

value.only 
Logical scalar, if 
The minimum stcut between source
and target
is the minimum
total weight of edges needed to remove to eliminate all paths from
source
to target
.
The minimum cut of a graph is the minimum total weight of the edges needed to remove to separate the graph into (at least) two components. (Which is to make the graph not strongly connected in the directed case.)
The maximum flow between two vertices in a graph is the same as the minimum
stcut, so max_flow
and min_cut
essentially calculate the same
quantity, the only difference is that min_cut
can be invoked without
giving the source
and target
arguments and then minimum of all
possible minimum cuts is calculated.
For undirected graphs the StoerWagner algorithm (see reference below) is used to calculate the minimum cut.
For min_cut
a numeric constant, the value of the minimum
cut, except if value.only = FALSE
. In this case a named list with
components:
value 
Numeric scalar, the cut value. 
cut 
Numeric vector, the edges in the cut. 
partition1 
The vertices in the first partition after the cut edges are removed. Note that these vertices might be actually in different components (after the cut edges are removed), as the graph may fall apart into more than two components. 
partition2 
The vertices in the second partition after the cut edges are removed. Note that these vertices might be actually in different components (after the cut edges are removed), as the graph may fall apart into more than two components. 
M. Stoer and F. Wagner: A simple mincut algorithm, Journal of the ACM, 44 585591, 1997.
max_flow
for the related maximum flow
problem, distances
, edge_connectivity
,
vertex_connectivity
g < make_ring(100) min_cut(g, capacity=rep(1,vcount(g))) min_cut(g, value.only=FALSE, capacity=rep(1,vcount(g))) g2 < graph( c(1,2,2,3,3,4, 1,6,6,5,5,4, 4,1) ) E(g2)$capacity < c(3,1,2, 10,1,3, 2) min_cut(g2, value.only=FALSE)