Trust networks consist of transitive trust relationships between people, organisations and software agents connected through a medium for communication and interaction. By formalising trust relationships, e.g. as reputation scores or as subjective trust measures, trust between parties within the community can be derived by analysing the trust paths linking the parties together. This article describes a method for trust network analysis using subjective logic (TNA-SL). It provides a simple notation for expressing transitive trust relationships, and defines a method for simplifying complex trust networks so that they can be expressed in a concise form and be computationally analysed. Trust measures are expressed as beliefs, and subjective logic is used to compute trust between arbitrary parties in the network. We show that TNA-SL is efficient, and illustrate possible applications with examples.