The paper investigates the problem of achieving scaled consensus within a finite time in edge dynamics of hybrid multi-agent systems over undirected and directed networks. The main challenge lies in achieving consensus under heterogeneous edge scaling and dynamic topologies. By modeling edge interactions via the line graph and introducing edge scaling through nonzero factors βij ≠ 0, we express the consensus behavior through a linear system representation. A CGM-based distributed algorithm is introduced to solve this system efficiently. According to the theoretical analysis, the algorithm reaches convergence in no more than M steps, with M being the edge count. Simulations confirm rapid convergence and improved accuracy over classical consensus protocols. The innovation lies in leveraging CGM for scalable, edge-based coordination with guaranteed finite-time performance.