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

Methods

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

Methods

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

Methods