In this paper, we consider the analysis and modelling of trust in distributed information systems. We review the relations of trust relationships in our previous work. We discuss trust layers and hierarchy based on formal definition of trust relationship. We provide a set of definitions to describe the properties of trust direction and trust symmetry under our taxonomy framework. In order to analyze and model the scope and diversity of trust relationship, we define trust scope label under our taxonomy framework. We provide some example scenarios to illustrate the proposed definitions about properties of trust relationship. The proposed definitions are new elements of the taxonomy framework for enabling the analysis and modelling of trust. We provide some discussions about the life cycle of trust relationships. The proposed trust structure and properties are currently being used in the development of the overall methodology of life cycle of trust relationships in distributed information systems.