Characteristic polynomial of a directed graph

Question

In eigenvalue decomposition ;prove that Coefficient $c_2$ in $P(λ)$ is equal to the number of edges multiplied by −1. where $P(λ)$ is the characteristic polynomial

$$P(λ) = \det ||A − λI|| = λ^N + c_1λ^{N−1} +· · ·+c_N.$$