Before revision:  These six desirable properties are formalized with the following guarantees: (1) The abstract and embedded trees represent the underlying graph appropriately at different level of details (in terms of the structure of the graph as well as the embedding thereof); ( 2  ) At every level of detail we show real vertices and real paths from the underlying graph;
After revision:  These six desirable properties are formalized with the following guarantees: (1) The abstract and embedded trees represent the underlying graph appropriately at different level of details ; ( 2 ) At every level of detail we show real vertices and real paths from the underlying graph;