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);
After revision:  These six desirable properties are formalized with the following guarantees: (1) The abstract 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);