Simulation program, plotting script, data, and finished plots to compile on a linux machine type "g++ -O3 -Wall main.c" Systems showing collective motion are partially described by a distribution of positions and a distribution of velocities. While models of collective motion often focus on system features governed mostly by velocity distributions, the model presented in this paper also incorpo- rates also features influenced by positional distributions. A significant feature, the size of the largest connected component of the graph in- duced by the particle positions and their perception range, is identified using a 1-d self-propelled particle model (SPP). Based on largest con- nected components, properties of the system dynamics are found that are time-invariant. A simplified macroscopic model can be defined based on this time-invariance, which may allow for simple, concise, and precise predictions of systems showing collective motion.