Use this if you are using igraph from R
A matching in a graph means the selection of a set of edges that are pairwise nonadjacenct, i.e. they have no common incident vertices. A matching is maximal if it is not a proper subset of any other matching.
is_matching(graph, matching, types = NULL) is_max_matching(graph, matching, types = NULL) max_bipartite_match( graph, types = NULL, weights = NULL, eps = .Machine$double.eps )
graph 
The input graph. It might be directed, but edge directions will be ignored. 
matching 
A potential matching. An integer vector that gives the
pair in the matching for each vertex. For vertices without a pair,
supply 
types 
Vertex types, if the graph is bipartite. By default they
are taken from the ‘ 
weights 
Potential edge weights. If the graph has an edge
attribute called ‘ 
eps 
A small real number used in equality tests in the weighted
bipartite matching algorithm. Two real numbers are considered equal in
the algorithm if their difference is smaller than 
is_matching
checks a matching vector and verifies whether its
length matches the number of vertices in the given graph, its values are
between zero (inclusive) and the number of vertices (inclusive), and
whether there exists a corresponding edge in the graph for every matched
vertex pair. For bipartite graphs, it also verifies whether the matched
vertices are in different parts of the graph.
is_max_matching
checks whether a matching is maximal. A matching
is maximal if and only if there exists no unmatched vertex in a graph
such that one of its neighbors is also unmatched.
max_bipartite_match
calculates a maximum matching in a bipartite
graph. A matching in a bipartite graph is a partial assignment of
vertices of the first kind to vertices of the second kind such that each
vertex of the first kind is matched to at most one vertex of the second
kind and vice versa, and matched vertices must be connected by an edge
in the graph. The size (or cardinality) of a matching is the number of
edges. A matching is a maximum matching if there exists no other
matching with larger cardinality. For weighted graphs, a maximum
matching is a matching whose edges have the largest possible total
weight among all possible matchings.
Maximum matchings in bipartite graphs are found by the pushrelabel algorithm with greedy initialization and a global relabeling after every n/2 steps where n is the number of vertices in the graph.
is_matching
and is_max_matching
return a logical
scalar.
max_bipartite_match
returns a list with components:
matching_size 
The size of the matching, i.e. the number of edges connecting the matched vertices. 
matching_weight 
The weights of the matching, if the graph was weighted. For unweighted graphs this is the same as the size of the matching. 
matching 
The matching itself. Numeric vertex id, or vertex
names if the graph was named. Nonmatched vertices are denoted by

Tamas Nepusz ntamas@gmail.com
g < graph_from_literal( abcdef ) m1 < c("b", "a", "d", "c", "f", "e") # maximal matching m2 < c("b", "a", "d", "c", NA, NA) # nonmaximal matching m3 < c("b", "c", "d", "c", NA, NA) # not a matching is_matching(g, m1) is_matching(g, m2) is_matching(g, m3) is_max_matching(g, m1) is_max_matching(g, m2) is_max_matching(g, m3) V(g)$type < c(FALSE,TRUE) print_all(g, v=TRUE) max_bipartite_match(g) g2 < graph_from_literal( abcdefg ) V(g2)$type < rep(c(FALSE,TRUE), length=vcount(g2)) print_all(g2, v=TRUE) max_bipartite_match(g2) #' @keywords graphs