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In graph-based modelled networks, connectivity and toughness are two types of parameters to measure the robustness of graphs (corresponding networks), and recent studies have shown that these variables are explicitly associated with the existence of H-factors in specific settings, where the latter is inner connected to the feasibility of data transmission in networks. However, the previous contributions presented in the form of several surfaces of connectivity and toughness (isolated toughness or sun toughness) lead to a "choice dilemma" for decision-makers in the network designing stage. In this work, to overcome this problem, we propose a new approach in terms of knee point identification to determine the best combination of connectivity and toughness related parameters. The family of knee points on curves are implemented which vary with respect to m or k. [ABSTRACT FROM AUTHOR]