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 an independent edge set, but the converse need not hold.
For example, two opposite edges of a four-vertex path graph form an 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.
