On the edges’ PageRank and line graphs

Two different approaches on a directed (and possibly weighted) network G are considered in order to define the PageRank of each edge of G with the focus on its applications. It is shown that both approaches are equivalent, even though it is clear that one approach has clear computational advantages over the other. The usefulness of this concept in the context of applications is illustrated by means of some examples within the area of cybersecurity and some simulations and examples within the scope of subway networks.