Given a graph $G=(E,V)$, I construct a graph $G'$ where the vertices of $G'$ are given by the edges of $G$ and say that two edges of $G$ are neighbors in $G'$ if they have a common vertex.


Is there a standard terminology for this construction, please? Is there a book/an article with all the standard properties of these graphs? 


I thank you much in advance.



What is the standard name of an edge-graph
The standard name for what you are describing is the *line graph* of $G$, however according to the *[wikipedia](http://en.wikipedia.org/wiki/Line_graph)* entry, it actually has been called the "edge graph" as well. While the wikipedia article is fairly extensive, you can also find information about line graphs in most graph theory textbooks, with perhaps [Harary's book](http://www.dtic.mil/dtic/tr/fulltext/u2/705364.pdf) the best place to start (Chapter 8). 


