Wastewater propagation chains (WPCs) measure inter-sector average propagation lengths (APL) of wastewater discharge. To achieve sustainable wastewater management, one needs to understand the propagation mechanisms by identifying WPCs at a national level over time. However, the traditional model of identifying WPCs is prone to retaining APLs with lower values but larger wastewater discharge intensities, ignoring many linkages whereby intensities are less than a preset threshold. Nevertheless, these overlooked linkages are valuable in understanding wastewater propagation mechanisms. This study proposed a new model coupled input-output analysis with the graphical theory, called the average propagation lengths-hub covariance graph (APL-HCG). This model can investigate WPCs where the closeness of sector linkages exceeds the preset thresholds. Furthermore, it is capable of retaining linkages for identifying hub wastewater propagation chains (HWPCs). Based on APL-HCG, the resultant HWPCs are decomposed as separated sub-chains which are basically composed of linkages among certain significant sectors belonging to the secondary industry or the tertiary industry. Scenario analyses show that HWPCs are effective in reducing wastewater discharge in the national economic system. The total wastewater discharge would decrease by 1.36%, 2.53%, 2.46%, and 2.11% if we reduced 10% of the final demand of all sectors in HWPCs in 2002, 2007, 2012, and 2017. The APL-HCG model outperforms the traditional model on WPCs by 0.14%, 1.61%, 0.47%, and 0.10%, respectively. The APL-HCG model is 0.21%, 0.68%, 0.70%, and 0.35% better than the scenario of random sampling with the number of sectors equal to HWPCs, respectively. Certain policy implications were provided to reduce wastewater effectively at the national level.
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