## table of contents

gfx(3) | Library Functions Manual | gfx(3) |

# 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*

*Inheritance*

*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*

*Inheritance*

*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*

*Inheritance*

*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.

AFNIX | AFNIX Module |