This study presents enhancements to a recently developed graph-based approach for the synthesis of vibration absorbers. The graph-based methodology is designed for the creation of minimal-complexity two-terminal passive vibration absorbers (PVAs) using spring-damper-inerter networks. It models PVAs as weighted, coloured multigraphs, enabling a systematic enumeration of all potential layouts for a given element type and count. Compared to the structure-immittance approach, this approach enables automated enumeration of PVA layouts. To address two key limitations of the published graph-based approach, several improvements have been introduced: (1) The use of numerical calculations, rather than symbolic operations, in graph redundancy checks – this modification significantly enhances computational efficiency; the advantage will become more pronounced as the number of elements increases. (2) By adopting a more structured algorithmic framework, the logic behind the enumeration process is clarified, ensuring that each step of the overall algorithm is modular and relatively independent - this structure also supports greater flexibility for expansion and broader applicability. The upgraded graph-based framework offers enhanced computational efficiency, readability and easiness for future adoption. This article primarily introduces the updated generation graph principles of this method, along with the corresponding redundancy elimination logic applied at each step. Finally, the effectiveness of the improved method is demonstrated through a quarter-car example.