 Induced subgraph

The subgraph induced by a vertex set $W$ contains every edge of the original graph whose two endpoints lie in $W$.

An **induced subgraph** is a concept from graph theory. Given a graph \( G = (V, E) \), where \( V \) is the set of vertices and \( E \) is the set of edges, an induced subgraph is formed by a subset of the vertices \( U \subseteq V \) along with all of the edges in \( E \) that have both endpoints in \( U \).