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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.
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A vertex a represents an endpoint of an edge. An edge joins two vertices a, b and is represented by set of vertices it connects. Here V is verteces and a, b, c, d are various vertex of the graph. Here E represents edges and {a, b}, {a, c}, {b, c}, {c, d} are various edge of the graph.
A directed graph, also called a digraph, is a graph in which the edges have a direction. This is usually indicated with an arrow on the edge; more formally, if v and w are vertices, an edge is an unordered pair {v,w}, while a directed edge, called an arc, is an ordered pair (v,w) or (w,v).
A vertex (or node) of a graph is one of the objects that are connected together. The connections between the vertices are called edges or links. A graph with 10 vertices (or nodes) and 11 edges (links). For more information about graph vertices, see the network introduction.
In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering (software construction and also software verification) to layout algorithms and picture generation.
LineGraph is a built-in function in Wolfram Language:
http://reference.wolfram.com/language/ref/LineGraph.html
This is what it does:
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