| Standard Graph Module

Standard graph services

This chapter covers the graph facilities available in the standard graph module. The basic operations are related to edge, vertices and graph manipulations.

All AFNIX standard graph objects are located in the `afnix-gfx` module. This module must be loaded prior any operation. Multiple calls to the module initialization routine are harmless. The interpreter method `module` loads a specific module by name. When the module has been loaded, the object are available in the `afnix:gfx` nameset.

Graph concepts

The `afnix-gfx` 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.

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.

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.

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.

Standard graph reference

This appendix is a reference of the AFNIX standard graph module.

Symbol | Description
--- | ---
afnix-gfx | module
afnix:gfx | nameset

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.