The literature on social networks has explored a large number of classes of human networks e.g., citation networks, online social networks, co-authorship networks, event networks, co-location networks, genealogy networks etc. The coverage of networks in the literature is however not uniform, one such neglected area is narrative networks. These networks constitute a class of networks which are formed by chains of narrations from one person to another person, these networks can even span generations. One of the reasons that the field has been neglected is because of the lack of datasets for analysis. In this paper an outline for the network science of narrative networks is given and a historical narrative network is constructed from a 9th century Middle Eastern source book. This network is used for network analysis and to illustrate the major problems in this field and lastly a set of research questions are proposed that should be addressed by researchers.