Formal Definition
Given a graph G, its line graph L(G) is a graph such that
- each vertex of L(G) represents an edge of G; and
- two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint ("are adjacent") in G.
That is, it is the intersection graph of the edges of G, representing each edge by the set of its two endpoints.
Read more about this topic: Line Graph
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