Hierarchical graph transformation

When graph transformation is used for programming purposes, large graphs should be structured in order to be comprehensible. In this paper, we present an approach for the rule-based transformation of hierarchically structured hypergraphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the well-known double-pushout approach from flat to hierarchical graphs. In particular, we show how pushouts and pushout complements of hierarchical graphs and graph morphisms can be constructed recursively. Moreover, we make rules more expressive by introducing variables which allow us to copy and remove hierarchical subgraphs in a single rule application.