  We investigate the behavior of active Brownian particles (ABP) within a
temporal complex network framework approach. We focused on the node degree
distribution, average path length, and average clustering coefficient across
the P\'eclet number and packing fraction region. In the single phase or gas
region, particle interactions mirror a random graph, and the average number of
unique interactions display a non-monotonic behavior with the packing fraction.
As we ventured toward the Motility-Phase Separation (MIPS) frontier, a hybrid
distribution with a time-evolving pattern emerged, combining Gaussian and power
law components. Moreover, we discovered a double power-law distribution in the
phase-separated region, with two characteristic slopes symbolizing the emerging
gas and solid regions. Our approach involved various numerical and theoretical
analyses to capture the role of the packing fraction and P\'eclet number in the
topological properties of the dynamical complex network that arises during the
ABP dynamics. These findings provide a robust understanding of a phase
transition between two states and how this transition manifests as a random to
scale-free behavior.
