Version 5.0 The LEDA User Manual

11.3 Static Graphs ( static graph )
1. Definition
1.1 Motivation. The data type static graph representing static graph is the result of
two observations:
First, most graph algorithms do not change the underlying graph, they work on a constant
or static graph and second, different algorithms are based on different models (we call
them categories) of graph.
The LEDA data type graph represents all types of graph used in the library, such as
directed, undirected, and bidirected graph, networks, planar maps, and geometric graph.
It provides the operations for all of these graph in one fat interface. For efficiency reasons
it makes sense to provide special graph data types for special purposes. The template data
type static graph, which is parameterized with the graph category, provides specialized
implementations for some of these graph types.
1.2 Static Graphs. A static graph consists of a fixed sequence of nodes and edges. The
parameterized data type static graph is used to represent
static graph. The first template parameter category defines the graph category and is
taken from {directed graph, bidirectional graph, opposite graph} (see 1.3 for the details).
The last two parameters are optional and can be used to define user-defined data structures
to be included into the node and edge objects (see 1.4 for the details). An instance G of
the parameterized data type static graph contains a sequence V of nodes and a sequence
E of edges. New nodes or edges can be appended only in a construction phase which has
to be started by calling G.start construction( ) and terminated by G.finish construction( ).
For every node or edge x we define index(x) to be equal to the rank of x in its sequence.
During the construction phase, the sequence of the source node index of all inserted edges
must be non-decreasing. After the construction phase both sequences V and E are fixed.
1.3 Graph Categories. We distinguish between five categories where currently only
the first three are supported by static graph:
• Directed Graphs (directed graph) represent the concept of a directed graph by providing
the ability to iterate over all edges incident to a given node v and to ask for
the target node of a given edge e.
• Bidirectional Graphs (bidirectional graph) extend directed graph by supporting in
addition iterations over all incoming edges at a given node v and to ask for the
source node of a given edge e.