  A complex unit gain graph is a graph where each orientation of an edge is
given a complex unit, which is the inverse of the complex unit assigned to the
opposite orientation. We extend some fundamental concepts from spectral graph
theory to complex unit gain graphs. We define the adjacency, incidence and
Laplacian matrices, and study each of them. The main results of the paper are
eigenvalue bounds for the adjacency and Laplacian matrices.
