This research presents two graphene-based terahertz (THz) patch antenna structures designed for THz applications. The unit cell of the antennas is made of graphene and silicon dioxide, with a dielectric permittivity of 3.7. The MIMO antenna operates at 0.6 THz, and its cells are arranged vertically. The reconfigurability of the antenna is achieved by changing the chemical potential or bias voltage of the graphene patches. The first antenna has an S$_{11}$ value less than -10 dB from 0.58786 THz to 0.63112 THz, with a maximum efficiency of about 65%. The second antenna has an S$_{11}$ value less than -10 dB from 0.57814 THz to 0.63391 THz, with a maximum efficiency of about 72%. The study also reports peak realized gains, radiation efficiencies, far-field 2D radiation patterns, VSWRs, current distributions, envelope correlation coefficients, and diversity gains over the operating frequency band for both antennas. The introduction highlights the significance of graphene-based quad-port MIMO reconfigurable antennas in telecommunication systems and wireless networks, particularly in satellite communications (SATCOMs) and 5G. These antennas enhance communication speed, network coverage, and capacity, improving user experience and data transfer. The advantages of these antennas include high data rates, reconfigurability, compact size, and low power consumption, making them suitable for portable and mobile applications.This research presents two graphene-based terahertz (THz) patch antenna structures designed for THz applications. The unit cell of the antennas is made of graphene and silicon dioxide, with a dielectric permittivity of 3.7. The MIMO antenna operates at 0.6 THz, and its cells are arranged vertically. The reconfigurability of the antenna is achieved by changing the chemical potential or bias voltage of the graphene patches. The first antenna has an S$_{11}$ value less than -10 dB from 0.58786 THz to 0.63112 THz, with a maximum efficiency of about 65%. The second antenna has an S$_{11}$ value less than -10 dB from 0.57814 THz to 0.63391 THz, with a maximum efficiency of about 72%. The study also reports peak realized gains, radiation efficiencies, far-field 2D radiation patterns, VSWRs, current distributions, envelope correlation coefficients, and diversity gains over the operating frequency band for both antennas. The introduction highlights the significance of graphene-based quad-port MIMO reconfigurable antennas in telecommunication systems and wireless networks, particularly in satellite communications (SATCOMs) and 5G. These antennas enhance communication speed, network coverage, and capacity, improving user experience and data transfer. The advantages of these antennas include high data rates, reconfigurability, compact size, and low power consumption, making them suitable for portable and mobile applications.