An edge-induced subgraph is a subset of the edges of a graph 
together with any vertices that are
their endpoints. The subgraph induced by a set of edges can be computed in the Wolfram Language using Subgraph[g,
elist].
Edge-Induced Subgraph
See also
Graph Minor, Induced Subgraph, Subgraph, Vertex-Induced SubgraphExplore with Wolfram|Alpha
References
Skiena, S. "Induced Subgraphs." §3.2.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 90-92, 1990.Referenced on Wolfram|Alpha
Edge-Induced SubgraphCite this as:
Weisstein, Eric W. "Edge-Induced Subgraph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Edge-InducedSubgraph.html