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With the emergence of network function virtualization (NFV), and software-defined networking (SDN), the realization and implementation of service function chains (SFCs) have become much easier. An SFC is an ordered set of interconnected virtual network functions (VNFs). NFV allows for decoupling the network functions from proprietary hardware realizing a software-based implementation of VNFs on commodity hardware and SDN decouples the network control from its forwarding logic allowing for a more flexible and programmable traffic routing among the VNFs. The SFC embedding problem (i.e. placement of SFCs on a shared substrate and establishing the corresponding traffic routes between the VNFs), has been extensively studied in the literature. In this paper, we extend a previous work on trust-aware service chain embedding with generalizing the role of trust by incorporating the trustworthiness of the service network links and substrate network paths into the SFC embedding decision process. We first introduce and formulate the path-based trust-aware service chain embedding problem as a mixed integer-linear program (MILP), and then provide an approximate model-based on selecting k-shortest candidate substrate paths for hosting each virtual link, to reduce the complexity of the model. We validate the performance of our methods through simulations and conduct a discussion on evaluating the methods and some operation trade-offs.