Network Function Virtualization (NFV) has emerged as an attractive technology solution to improve the efficiency and flexibility of network services through a technique called Service Chain mapping. A Network Service may be composed of several components (sub-services) and a subset of the physical network nodes may be able to provide each of the individual sub-services. The goal of the Service Chain Mapping problem is to select a physical network node to get the individual sub-services executed and making sure that results from execution of one sub-service flows smoothly to the physical node selected for execution of the next sub-service. Recently, there is increasing awareness in the research community that there exists significant dependency between network nodes. In order to seamlessly deal with failures, provisions are made for redundant services (and sub-services). However, unless the Service Chain mapping is carried out carefully, both the primary and the backup service providers may be unavailable due to the failure of one single physical node. Even if the backup service provider is available, the increased delay to access the backup node may be unacceptably high. Recognizing the importance of structural dependency, researchers have recently started studying dependency-aware Service Chain mapping. In this paper, we draw attention to some of the shortcomings of a recently proposed metric for measuring structural dependency. In addition, we introduce a notion of utility of a path for data transfer from a source node u to a destination node v, to provide a dynamic programming based algorithm for mapping a service chain on a physical network which ensures that the loss of utility due to failure of physical network nodes is minimized.