## 5.6. What we did not cover

*Learning objectives*

The class `ugraph` |

The classes `node_matrix` and `node_map2` |

Static graphs |

The classes `face_array` and `face_map` |

The classes `planar_map` and `PLANAR_MAP` |

Functions templatized with number types |

The gml format |

The class `ugraph`

implements undirected graphs. It is primarily used by LEDA's
internal algorithms and should not be used in programs of one's
own, just because the interfaces of LEDA's built-in graph
algorithms all expect a `graph`

as input.

### The classes `node_matrix`

and `node_map2`

The class `node_matrix`

expands the concept of `node_array`

to
two-dimensional index sets. (Both indices are nodes.) It
appears, for example, as the type of a parameter of the function
`ALL_PAIRS_SHORTEST_PATHS()`

that defines the
distance of each node to each other node. Likewise, the class
`node_map2`

expands the concept of the class `node_map`

to two-dimensional index sets.

As of version 4.5 of LEDA, there is a particularly
efficient class of its own for static graphs, that is, for
graphs that do not change any more after their construction
phase. The corresponding manual page
contains more information about this graph type.

### The classes `face_array`

and `face_map`

The classes `face_array`

and `face_map`

allow to associate information to the faces of a map.

### The classes `planar_map`

and `PLANAR_MAP`

The class `planar_map`

is useful for managing combinatorial
embeddings of planar graphs, as we came to know them in Section 5.2.6.

The class `PLANAR_MAP`

allows to associate additional information to the
nodes, edges, and faces of a planar map.

### Functions templatized with number types

Many functions from `shortest_path.h`

,
`max_flow.h`

,
`mwb_matching.h`

, and
`mw_matching.h`

are also available in a
templatized version in which the number type of the edge
information can be specified (and therefore does not necessarily
have to be `int`

). By using a number type with a larger
definition domain and/or a higher precision, methodically
induced rounding errors can be lowered.

Beside the standard
format for storing graphs (file extension
`.gw`

), there is also, by historical reasons,
the *gml format* (file
extension `.gml`

).