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<!-- = copyright (c) 1999-2007 - amaury darsch = -->
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<chapter module="gfx" number="1">
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<title>Standard graph services</title>
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This chapter covers the graph facilities available in the
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<em>standard graph</em> module. The basic operations are related to
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edge, vertices and graph manipulations.
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All <afnix/> standard graph objects are located in the
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<code>afnix-gfx</code> module. This module must be loaded prior
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any operation. Multiple calls to the module initialization routine
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are harmless. The interpreter method <code>module</code> loads a
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specific module by name. When the module has been loaded, the
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object are available in the <code>afnix:gfx</code> nameset.
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interp:library "afnix-gfx"
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<title>Standard graph module</title>
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This chapter covers the graph facilities available in the
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<em>standard graph</em> module. The basic operations are related to
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edge, vertices and graph manipulations.
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<!-- graph concepts -->
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<title>Graph concepts</title>
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The <code>afnix-gfx</code> provides the support for manipulating
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graphs. Formally a graph is a collection of edges and vertices. In
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a normal graph, an edge connects two vertices. On the other hand,
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a vertex can have several edges. When an edge connects several
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vertices, it is called an hyperedge and the resulting structure is
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The <code>afnix-gfx</code> module provides the support for manipulating
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graphs. Formally a graph is a collection of edges and vertices. In
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a normal graph, an edge connects two vertices. On the other hand,
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a vertex can have several edges. When an edge connects several
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vertices, it is called an hyperedge and the resulting structure is
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<!-- edge class -->
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<title>Edge class</title>
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The <code>Edge</code> class is a class used for a graph
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construction in association with the <code>Vertex</code> class.
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An edge is used to connect vertices. Normally, an edge connects
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two vertices. The number of vertices attached to an edge is
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called the cardinality of that edge. When the edge cardinality
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is one, the edge is called a self-loop. This mean that the edge
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connects the vertex to itself. This last point is merely a
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definition but present the advantage of defining an hyperedge as
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The <code>Edge</code> class is a class used for a graph
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construction in association with the <code>Vertex</code> class.
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An edge is used to connect vertices. Normally, an edge connects
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two vertices. The number of vertices attached to an edge is
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called the cardinality of that edge. When the edge cardinality
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is one, the edge is called a self-loop. This mean that the edge
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connects the vertex to itself. This last point is merely a
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definition but present the advantage of defining an hyperedge as
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<title>Vertex class </title>
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The <code>Vertex</code> is the other class used for the
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graph construction. and operates with the <code>edge</code>
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class. A vertex is used to reference edges. the number of edges
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referenced by a vertex is called the degree of that vertex.
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The <code>Vertex</code> is the other class used for the
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graph construction. and operates with the <code>edge</code>
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class. A vertex is used to reference edges. the number of edges
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referenced by a vertex is called the degree of that vertex.
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<title>Graph</title>
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The <code>Graph</code> class is class that represent either a
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graph or a hypergraph. By definition, a graph is collection of
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edges and vertices. There are numerous property attached to
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graph. Formally, a graph consists of a set of edges, a set of
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vertices and the associated endpoints. However, the implementation
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is designed in a way so that each edge and vertex carry its
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associated objects. This method ensures that the graph is fully
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defined by only its two sets.
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The <code>Graph</code> class is class that represent either a
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graph or a hypergraph. By definition, a graph is collection of
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edges and vertices. There are numerous property attached to
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graph. Formally, a graph consists of a set of edges, a set of
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vertices and the associated endpoints. However, the implementation
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is designed in a way so that each edge and vertex carry its
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associated objects. This method ensures that the graph is fully
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defined by only its two sets.
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<title>Graph construction</title>
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The graph construction is quite simple and proceed by adding edges
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and vertices. The base system does not enforce rules on the graph
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structure. it is possible to add con connected vertices as well as
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The graph construction is quite simple and proceed by adding edges
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and vertices. The base system does not enforce rules on the graph
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structure. it is possible to add con connected vertices as well as
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<!-- edge construction -->
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<title>Edge construction</title>
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An edge is constructed by simply invoking the default
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constructor. Optionally, a client object can be attached to the
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An edge is constructed by simply invoking the default
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constructor. Optionally, a client object can be attached to the
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# create a default edge
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const edge (afnix:gfx:Edge)
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# create an edge with a client object
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const hello (afnix:gfx:Edge "hello")
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# create a default edge
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const edge (afnix:gfx:Edge)
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# create an edge with a client object
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const hello (afnix:gfx:Edge "hello")
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The <code>edge-p</code> predicate can be used to check for the
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object type. When an edge is created with client object, the
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<code>get-client</code> method can be used to access that object.
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The <code>edge-p</code> predicate can be used to check for the
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object type. When an edge is created with client object, the
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<code>get-client</code> method can be used to access that object.
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<title>Vertex construction</title>
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A vertex is constructed a way similar to the <code>Edge></code>
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object. The vertex is constructed by simply invoking the default
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constructor. Optionally, a client object can be attached to the
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A vertex is constructed a way similar to the <code>Edge></code>
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object. The vertex is constructed by simply invoking the default
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constructor. Optionally, a client object can be attached to the
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# create a default vertex
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const vrtx (afnix:gfx:Vertex)
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# create an vertex with a client object
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const world (afnix:gfx:Vertex "world")
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# create a default vertex
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const vrtx (afnix:gfx:Vertex)
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# create an vertex with a client object
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const world (afnix:gfx:Vertex "world")
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The <code>vertex-p</code> predicate can be used to check for the
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object type. When a vertex is created with a client object, the
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<code>get-client</code> method can be used to access that object.
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The <code>vertex-p</code> predicate can be used to check for the
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object type. When a vertex is created with a client object, the
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<code>get-client</code> method can be used to access that object.
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<title>Graph construction</title>
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A graph is constructed by simply adding edges and vertices to
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it. The <code>graph-p</code> predicate can be use to assert the
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graph type. the graph class also supports the concept of client
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object which can be attached at construction or with the
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<code>set-client</code> method.
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A graph is constructed by simply adding edges and vertices to
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it. The <code>graph-p</code> predicate can be use to assert the
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graph type. the graph class also supports the concept of client
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object which can be attached at construction or with the
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<code>set-client</code> method.
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const graph (afnix:gfx:Graph)
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const graph (afnix:gfx:Graph)
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The <code>add</code> method can be used to add edges or vertices
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to the graph. The important point is that during the
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construction process, the graph structure is updated with the
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proper number of edge and vertices.
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The <code>add</code> method can be used to add edges or vertices
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to the graph. The important point is that during the
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construction process, the graph structure is updated with the
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proper number of edge and vertices.
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const g (afnix:gfx:Graph)
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assert true (afnix:gfx:graph-p g)
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# create an edge and add vertices
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const edge (afnix:gfx:Edge)
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edge:add (afnix:gfx:Vertex "hello")
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edge:add (afnix:gfx:Vertex "world")
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assert 2 (edge:degree)
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# add the edge to the graph and check
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assert 1 (g:number-of-edges)
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assert 2 (g:number-of-vertices)
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# check for nodes and edges
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assert true (afnix:gfx:edge-p (g:get-edge 0))
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assert true (afnix:gfx:vertex-p (g:get-vertex 0))
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assert true (afnix:gfx:vertex-p (g:get-vertex 1))
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const g (afnix:gfx:Graph)
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assert true (afnix:gfx:graph-p g)
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# create an edge and add vertices
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const edge (afnix:gfx:Edge)
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edge:add (afnix:gfx:Vertex "hello")
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edge:add (afnix:gfx:Vertex "world")
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assert 2 (edge:degree)
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# add the edge to the graph and check
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assert 1 (g:number-of-edges)
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assert 2 (g:number-of-vertices)
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# check for nodes and edges
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assert true (afnix:gfx:edge-p (g:get-edge 0))
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assert true (afnix:gfx:vertex-p (g:get-vertex 0))
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assert true (afnix:gfx:vertex-p (g:get-vertex 1))
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src/mod/gfx/doc/chapter-1.xml
