NAME

       gfx - standard graph module

STANDARD GRAPH MODULE

       The  Standard  Graph module is an original implementation dedicated to the graph moddeling
       and manipulation. At the heart of this module is the concept of edges and vertices.

       Graph concepts
       The afnix-gfx module provides the support for manipulating graphs. Formally a graph  is  a
       collection of edges and vertices. In a normal graph, an edge connects two vertices. On the
       other hand, a vertex can have several edges. When an edge connects several vertices, it is
       called an hyperedge and the resulting structure is called an hypergraph.

       Edge class
       The  Edge  class  is  a class used for a graph construction in association with the Vertex
       class. An edge is used to connect vertices. Normally, an edge connects two  vertices.  The
       number  of  vertices  attached to an edge is called the cardinality of that edge. When the
       edge cardinality is one, the edge is called a self-loop. This mean that the edge  connects
       the  vertex to itself. This last point is merely a definition but present the advantage of
       defining an hyperedge as a set of vertices.

       Vertex class
       The Vertex is the other class used for the graph construction. and operates with the  edge
       class.  A vertex is used to reference edges. the number of edges referenced by a vertex is
       called the degree of that vertex.

       Graph
       The Graph class is class that represent either a graph or a hypergraph. By  definition,  a
       graph  is collection of edges and vertices. There are numerous property attached to graph.
       Formally, a graph consists of a set of  edges,  a  set  of  vertices  and  the  associated
       endpoints.  However,  the implementation is designed in a way so that each edge and vertex
       carry its associated objects. This method ensures that the graph is fully defined by  only
       its two sets.

       Graph construction
       The  graph construction is quite simple and proceed by adding edges and vertices. The base
       system does not enforce rules on the graph structure. it is possible to add con  connected
       vertices as well as unreferenced edges.

       Edge construction
       An  edge  is  constructed by simply invoking the default constructor. Optionally, a client
       object can be attached to the edge.

       # create a default edge
       const edge (afnix:gfx:Edge)
       # create an edge with a client object
       const hello (afnix:gfx:Edge "hello")

       The edge-p predicate can be used to check for the object type. When  an  edge  is  created
       with client object, the get-client method can be used to access that object.

       Vertex construction
       A  vertex  is  constructed a way similar to the Edge> object. The vertex is constructed by
       simply invoking the default constructor. Optionally, a client object can  be  attached  to
       the edge.

       # create a default vertex
       const vrtx (afnix:gfx:Vertex)
       # create an vertex with a client object
       const world (afnix:gfx:Vertex "world")

       The  vertex-p predicate can be used to check for the object type. When a vertex is created
       with a client object, the get-client method can be used to access that object.

       Graph construction
       A graph is constructed by simply adding edges and vertices to it.  The  graph-p  predicate
       can  be  use to assert the graph type. the graph class also supports the concept of client
       object which can be attached at construction or with the set-client method.

       const graph (afnix:gfx:Graph)

       The add method can be used to add edges or vertices to the graph. The important  point  is
       that  during  the  construction  process,  the  graph structure is updated with the proper
       number of edge and vertices.

       # create a graph
       const  g    (afnix:gfx:Graph)
       assert true (afnix:gfx:graph-p g)
       # create an edge and add vertices
       const edge (afnix:gfx:Edge)
       edge:add   (afnix:gfx:Vertex "hello")
       edge:add   (afnix:gfx:Vertex "world")
       assert 2   (edge:degree)
       # add the edge to the graph and check
       g:add edge
       assert 1 (g:number-of-edges)
       assert 2 (g:number-of-vertices)
       # check for nodes and edges
       assert true (afnix:gfx:edge-p   (g:get-edge   0))
       assert true (afnix:gfx:vertex-p (g:get-vertex 0))
       assert true (afnix:gfx:vertex-p (g:get-vertex 1))

STANDARD GRAPH REFERENCE

       Edge
       The Edge class is a class used for a graph construction in  association  with  the  Vertex
       class.  An  edge is used to connect vertices. Normally, an edge connects two vertices. The
       number of vertices attached to an edge is called the cardinality of that  edge.  A  client
       object can also be attached to the class.

       Predicate

              edge-p

       Inheritance

              Object

       Constructors

              Edge (none)
              The Edge constructor create an empty edge.

              Edge (Object)
              The Edge constructor create an edge with a client object.

       Methods

              reset -> none (none)
              The reset method reset all vertices attached to the edge.

              cardinality -> Integer (none)
              The  cardinality  method returns the cardinality of the edge. The cardinality of an
              edge is the number of attached vertices.

              add -> Vertex (Vertex)
              The add method attach a vertex to this edge. The method return the argument vertex.

              get -> Vertex (Integer)
              The get method returns the attached vertex by index. If the index is out-of  range,
              and exception is raised.

              get-client -> Object (none)
              The  get-client  method returns the edge client object. If the client object is not
              set, nil is returned.

              set-client -> Object (Object)
              The set-client method sets the edge client object. The object is returned  by  this
              method.

       Vertex
       The  Vertex  class  is  a class used for a graph construction in association with the Edge
       class. An vertex is an edge node. The number of edges referenced by a vertex is called the
       degree of that vertex. A client object can also be attached to the object.

       Predicate

              vertex-p

       Inheritance

              Object

       Constructors

              Vertex (none)
              The Vertex constructor create an empty vertex.

              Vertex (Object)
              The Vertex constructor create a vertex with a client object.

       Methods

              reset -> none (none)
              The reset method reset all edges attached to the vertex.

              degree -> Integer (none)
              The  degree  method returns the degree of the vertex. The degree of a vertex is the
              number of referenced edges.

              add -> Edge (Edge)
              The add method references an edge with this vertex. The method return the  argument
              edge.

              get -> Edge (Integer)
              The  get method returns the referenced edge by index. If the index is out-of range,
              and exception is raised.

              get-client -> Object (none)
              The get-client method returns the vertex client object. If the client object is not
              set, nil is returned.

              set-client -> Object (Object)
              The set-client method sets the vertex client object. The object is returned by this
              method.

       Graph
       The Graph object is a general graph class that manages a set of edges  and  vertices.  The
       graph  operates by adding edges and vertices to it. The graph object also accepts a client
       object in a way similar to the Edge and Vertex classes

       Predicate

              graph-p

       Inheritance

              Object

       Constructors

              Graph (none)
              The Graph constructor create an empty graph.

              Graph (Object)
              The Graph constructor create a graph with a client object.

       Methods

              reset -> none (none)
              The reset method reset the graph

              reset-edges -> none (none)
              The reset-edges method reset all edges attached to the graph.

              reset-vertices -> none (none)
              The reset-vertices method reset all vertices attached to the graph.

              add -> Object (Vertex|Edge)
              The add method adds a vertex or an edge to the graph.  When  adding  an  edge,  the
              methods check that the source and target vertices are also part of the graph.

              exists -> Boolean (Vertex|Edge)
              The exists method returns true if the vertex or edge argument exists in the graph.

              get-edge -> Edge (Integer)
              The  get-edge  method  returns  an  edge by index. If the index is out-of-range, an
              exception is raised.

              get-vertex -> Vertex (Integer)
              The get-vertex method returns a vertex by index. If the index is  out-of-range,  an
              exception is raised.

              number-of-vertices -> Integer (none)
              The number-of-vertices methods returns the number of vertices in the graph.

              number-of-edges -> Integer (none)
              The number-of-edges methods returns the number of edges in the graph.

              get-client -> Object (none)
              The  get-client method returns the graph client object. If the client object is not
              set, nil is returned.

              set-client -> Object (Object)
              The set-client method sets the graph client object. The object is returned by  this
              method.