When transacting and interacting through open computer networks, traditional methods used in the physical world for establishing trust can no longer be used. Creating virtual network substitutes with which people, organisations and software agents can derive trust in other parties requires computerised analysis of the underlying trust networks. This article describes an approach to trust network analysis using subjective logic (TNA-SL), that consists of the three following elements. Firstly it uses a concise notation with which trust transitivity and parallel combination of trust paths can be expressed. Secondly it defnes a method for simplifying complex trust networks so that they can be expressed in this concise form. Finally it allows trust measures to be expressed as beliefs, so that derived trust can be automatically and securely computed with subjective logic. We compare our approach with trust derivation algorithms that are based on normalisation such as PageRank and EigenTrust. We also provide a numerical example to illustrates how TNA-SL can be applied.