  In this paper, we investigate a five-dimensional Dirac fermion on a quantum
graph that consists of a single vertex and $N$ loops. We find that the model
possesses a rich structure of boundary conditions for wavefunctions on the
quantum graph and they can be classified into $(2N+1)$ distinct categories. It
is then shown that there appear degenerate four-dimensional chiral massless
fermions in the four-dimensional mass spectrum. We briefly discuss how our
model could naturally solve the problems of the fermion generation, the fermion
mass hierarchy and the origin of the $CP$-violating phase.
