I understand the concept of induced subgraph, but could not understan what induced matching is. As appears in this paper, it is defined as
A matching in a graph is an induced matching if it occurs as an induced subgraph of the graph.
However, in this paper, there is a slightly different definition:
A matching in a graph is a set of edges, no two of which meet a common vertex. An induced matching M in a graph G is a matching where no two edges of M are joined by an edge of G.
Thus, I am confused since there are no example figures.
Also, there is a term called mim-width, which is maximum induced matching width and few no none examples exist in the literature.
Could you please give some examples for me to clear things out?