Terahertz (0.06-10 THz) band communication is envisioned as a key technology to satisfy the increasing demand for ultrahigh-speed wireless links. In this paper, a distance-aware bandwidth-adaptive resource allocation scheme is developed for THz band communication networks, which has the objective to improve the distance. The proposed scheme captures the unique channel peculiarities including the relationship between the distance and the bandwidth, and strategically utilizes the spectrum to enable multiple ultrahigh-speed links. Based on the developed scheme, the subwindows of the THz spectrum, the modulations, and the transmit power are adaptively allocated, for both singleuser and multiuser communications. The numerical results show that the developed resource allocation scheme improves the distances and exploitation of the THz spectrum significantly. Specifically, 10 Gb/s can be supported at 4 m in the multipath channel, while 100 Gb/s is achieved up to 21 m in the line-of-sight transmission with the use of 20 dB gain antennas. Furthermore, in the multiuser network, 14 10 Gb/s links can be supported simultaneously in the multipath channel. With the use of 20 dB gain antennas, 13 100 Gb/s links can be supported at the same time. Moreover, the developed resource allocation scheme outperforms the existing millimeter-wave systems and the nonadaptive scheme. This paper achieves the design objective and contributes to enable multiple ultrahigh-speed links in the THz band communication network.