An induced matching in a simple graph is an independent edge set whose endpoints induce no edges other than those in the set. Thus endpoints belonging to different selected edges are neither equal nor adjacent. Every induced matching is a independent edge set, but the converse need not hold.
For example, two opposite edges of a four-vertex path graph form a independent
edge set but not an induced matching. In a path graph 
, the largest induced matching has
edges
for 
,
where 
is the floor function. A complete
bipartite graph with both parts nonempty has largest induced matching of size
1, irrespective of its ordinary matching number.
Induced matchings intersecting bags of a tree decomposition define the induced matching treewidth.
