Parametric Graph Theory and Matrix Approach (GTMA) Model for Assessing the Surface Water Quality

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Mansoor Ahmad Baluch


In this paper a systematic parametric approach for assessing the water quality for given water resource by using the concepts of graph theory and matrix algebra is presented. A new, novel, generic and more sensitive water quality index (WQI) named as “Baluch” index is proposed that can assess and ranks the water quality for a given water resource. The water quality parameters listed in FAO-29 guidelines (belong to resource under investigation) and their relative importances are utilized to create a water quality assessment graph (WQG) and adjacency matrix. As a case study, the water quality of eighteen stations of upper basin of Indus River, Pakistan is assessed. Eight physico-chemical quality parameters including pH, TDS, Total hardness,  Ca Hardness, Mg hardness, SO4-2, Cl-1, and EC are used for constructing WQA. This WQA is then used to figure out “Baluch” index for each monitoring station, and it is found that “Baluch” index for Darband station has lowest value i.e. 0.85 and “Baluch” index highlight the situation that all other stations have relatively higher values of pH, which is concern able problem. Furthermore, this new index indicate the lowest quality water belongs to Jijal stations due relatively higher values of pH (i.e. 8.25) and Cl- ion, above average values of TDS, Harness, SO42- ion concentrations.

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Baluch, M. (2022). Parametric Graph Theory and Matrix Approach (GTMA) Model for Assessing the Surface Water Quality. Technical Journal, 27(02), 10-19. Retrieved from

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