  Carbon nitride compounds have emerged recently as a prominent member of 2D
materials beyond graphene. The experimental realizations of 2D graphitic carbon
nitride g-C$_3$N$_4$, nitrogenated holey grahpene C$_2$N, polyaniline C$_3$N
have shown their promising potential in energy and environmental applications.
In this work, we predict a new type of carbon nitride network with a C$_9$N$_4$
stoichiometry from first principle calculations. Unlike common C-N compounds
and covalent organic frameworks (COFs), which are typically insulating,
surprisingly C$_9$N$_4$ is found to be a 2D nodal-line semimetal (NLSM). The
nodal line in C$_9$N$_4$ forms a closed ring centered at $\Gamma$ point, which
originates from the pz orbitals of both C and N. The linear crossing happens
right at Fermi level contributed by two sets of dispersive Kagome and Dirac
bands, which is robust due to negligible spin-orbital-coupling (SOC) in C and
N. Besides, it is revealed that the formation of nodal ring is of accidental
band degeneracy in nature induced by the chemical potential difference of C and
N, as validated by a single orbital tight-binding model, rather than protected
by crystal in-plane mirror symmetry or band topology. Interestingly, a new
structure of nodal line, i.e., nodal-cylinder, is found in momentum space for
AA-stacking C$_9$N$_4$. Our results imply possible functionalization for a
novel metal-free C-N covalent network with interesting semimetallic properties.
