As XML is gathering more and more importance in the field of data interchange in distributed business to business (B2B) applications, it is increasingly important to provide a formal definition of XML-structures together with a well defined way to map business domain semantics to these structures. An XML-algebra, similar to the relational algebra, is required for the formal definition of operations and transformations and to prove the correctness and completeness of design methods. To develop an XML algebra, we propose a sound mathematical foundation, modeling XML-structures as typed directed graphs based on set theory. Together with a formal method to apply domain semantics to directed graphs we present a three layer meta model to address the separation of structure and content, and we introduce extensible type hierarchies on nodes and links. This allows to model and validate business domain semantics on different levels of abstraction.