Graph transformation - vertices into edges and edges into vertices

Question

is there any algorithm or is there any name for a transformation of a graph where one can transform edges into vertices and vertices into edges? Just so we could get a new graph out of it or anything similiar to this problem? I'm not sure if it actually makes sense but I'd be glad if you could give me just any hint about a problem like this.

Answer 1

LineGraph is a built-in function in Wolfram Language:

http://reference.wolfram.com/language/ref/LineGraph.html

This is what it does:

• Each vertex in LineGraph[g] corresponds to an edge in g.
• For an undirected graph g, two vertices in LineGraph[g] are adjacent if their corresponding edges share a common vertex.
• For a directed graph g, two vertices in LineGraph[g] are adjacent if their corresponding edges are connected, i.e. the target of one edge is the source of the other edge.
• LineGraph works with undirected graphs, directed graphs, and multigraphs.