Distance measures for embedded graphs

We introduce new distance measures for comparing straight-line embedded graphs based on the Fréchet and weak distance. These graph distances are defined using continuous mappings thus take combinatorial structure as well geometric embeddings of into account. present a general algorithmic approach computing these distances. Although we show that deciding is NP-hard graphs, prove our yields polynomial time algorithms if trees, planar embedding meets certain restriction. Moreover, remains how an exponential algorithm approximation this case.