Subgraph

Definition

A subgraph of a Graph $G=(V,E)$ is another graph formed from a subset of the vertices and edges of $G$.

Node-Induced Subgraph

Take subset of the nodes and all edges induced by the nodes.

$G^{\prime }=(V^{\prime },E^{\prime })$ where $V^{\prime }\subset V$ and $E^{\prime }=\{(u,v)\in E|u,v\in V^{\prime }\}$.

Edge-Induced Subgraph

Take subset of the edges and all corresponding nodes. $G^{\prime }=(V^{\prime },E^{\prime })$ where $E^{\prime }\subset E$ and $V^{\prime }=\{u,v\in V|(u,v)\in E^{\prime }\}$.