This paper investigates the impact of rigid communication topologies (RCTs) on the performance of vehicular platoons, aiming to identify beneficial features in RCTs that enhance vehicles behavior. We introduce four performance metrics, focusing on safety, energy consumption, passenger comfort, and robustness of vehicular platoons. The safety metric is based on momentary distances between neighboring vehicles, their relative velocities, and relative accelerations. Thus, to have access to these relative values, we formulate the coupled dynamics between pairs of neighboring vehicles, considering initial conditions (position, velocity, acceleration), leader vehicle's velocity/acceleration trajectory, deployed RCT, and vehicles' parity/disparity. By decoupling the dynamics using a mapping matrix structured on deployed RCT, vehicles' features, and control gains, precise formulations for distance errors, relative velocities, and relative accelerations between all neighboring vehicles, over the travel time, are obtained. Comparing performance metric results across RCTs highlights that downstream information transmission-from vehicles ahead, particularly the leader vehicle, to vehicles behind-significantly enhances platoon stability, safety, energy consumption, and passenger comfort metrics. Conversely, receiving state information from vehicles behind degrades metrics, compromising safety, increasing energy consumption, and reducing passenger comfort. These findings underscore that forward-looking, leader-centric communications between vehicles markedly enhance platoon efficiency and safety.