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 connecting pairs of vertices in that subset.

Definition

Formally, let be any graph, and let be any subset of vertices of. Then the induced subgraph is the graph whose vertex set is and whose edge set consists of all of the edges in that have both endpoints in. The same definition works for undirected graphs, directed graphs, and even multigraphs.
The induced subgraph may also be called the subgraph induced in by, or the induced subgraph of .

Examples

Important types of induced subgraphs include the following.
problem concerns the longest induced paths in hypercube graphs
The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the goal is to test whether one graph can be found as an induced subgraph of another. Because it includes the clique problem as a special case, it is NP-complete.