We present the Chromatic Persistence Algorithm (CPA), an event–driven method for computing persistent cohomological features of weighted graphs via graphic arrangements, a classical object in computational geometry. We establish rigorous complexity results: CPA is exponential in the worst case, fixed–parameter tractable in treewidth, and nearly linear for common graph families such as trees, cycles, and series–parallel graphs. Finally, we demonstrate its practical applicability through a controlled experiment on molecular-like graph structures.