The problem that we would like to solve in this paper is to compute the edge p-Laplacian centrality for the air traffic network. In this problem, instead of computing the edge p-Laplacian centrality directly which is the very hard problem, we convert the air traffic network to the line graph. Finally, we will compute the node p-Laplacian centrality of the line graph which is equivalent to the edge p-Laplacian of the air traffic network. In this paper, the novel un-normalized graph (p-) Laplacian based ranking method will be developed based on the un-normalized graph p-Laplacian operator definitions such as the curvature operator of graph (i.e. the un-normalized graph 1-Laplacian operator) and will be used to compute the node p-Laplacian centrality of the line graph. The results from the experiments show that the un-normalized graph p-Laplacian ranking methods can be implemented successfully.