This paper focuses on the spatial-spectral terahertz (THz) networks, where transmitters equipped with leaky-wave antennas send information to their receivers at the THz frequency bands. As a directional and nearly planar antenna, the leaky-wave antenna allows for information transmissions with narrow beams and high antenna gains. The conventional large antenna arrays are confronted with challenging issues such as scaling limits and path discovery in the THz frequencies. Therefore, this work exploits the potential of leaky-wave antennas in the dense THz networks, to establish low-complexity THz links. By addressing the propagation angle-frequency coupling effects, the transmission rate is analyzed. The results show that the leaky-wave antenna is efficient for achieving the high-speed transmission rate. The co-channel interference management is unnecessary when the THz transmitters with large subchannel bandwidths are not extremely dense. A simple subchannel allocation solution is proposed, which enhances the transmission rate compared with the same number of subchannels with the equal allocation of the frequency band. After subchannel allocation, a low-complexity power allocation method is proposed to improve the energy efficiency.