The application of graph theory for vulnerability assessment in service triads

A supply chain triad is increasingly regarded as a unit of analysis of complex supply chain networks, allowing the realization of properties such as certain risks manifesting at the level of supply chain networks, and which are not necessarily observed at the level of supply chain dyads or individual supply chain partners. This study investigates a type of supply chain triad - service triads - and explores cross- organizational pathways according to which risks can emerge and propagate within such triadic structures. The aim of the study is to design an analytical model with the view to facilitate the assessment of vulnerability in service triads according to the aforementioned cross-organizational pathways of risk emergence and propagation. Using graph theory, a range of service triad reference models are developed, which formalize the typology and direction of the relationships between members of the supply chain triad. Adopting the notion of matrix permanent allows calculating the vulnerability levels of distinct service triad models, accounting for the formalized typology and direction of the relationships within the models. A case study in a corporate bonds context is conducted to illustrate the applicability of the proposed approach to vulnerability assessment in the service industry context.