Induced subgraph
In graph theory, an induced subgraph of a graph is another graph, formed from a subset of the vertices of the graph and all of the edges, from the original graph, connecting pairs of vertices in that subset. == Definition == Formally, let G = ( V , E ) {\displaystyle G=(V,E)} be any graph, and let S ⊆ V {\displaystyle S\subseteq V} be any subset of vertices of G. Then the induced subgraph G [ S ] {\displaystyle G[S]} is the graph whose vertex set is S {\displaystyle S} and whose edge set consists of all of the edges in E {\displaystyle E} that have both endpoints in S {\displaystyle S} .