Create a new graph of type `graph-type'. Graph type can be a symbol naming a sub-class of basic-graph or a list. If it is a list of symbols naming different classes. If graph-type is a list, then a class which has all of the listed classes as superclasses will be found (or created). In either case, the new graph will be created as if with a call to make-instance.

Adds a vertex to a graph. If called with a vertex, then this vertex is added. If called with a value, then a new vertex is created to hold the value. If-duplicate-do can be one of :ignore, :force, :replace, :replace-value, :error, or a function. The default is :ignore.

Add-edge adds an existing edge to a graph. As add-edge-between-vertexes is generally more natural to use, this method is rarely called.

Adds an edge between two vertexes and returns it. If force-new? is true, the edge is added even if one already exists. If the vertexes are not found in the graph, they will be added (unless :error-if-not-found? is true). The class of the edge can be specified using :edge-class or :edge-type. If :edge-type is used, it can be either :directed or :undirected; the actual class of the edge will be determined by using the edge-types of the graph. If neither :edge-type nor :edge-class is specified, then a directed edge will be created.

If-duplicate-do is used when the 'same' edge is added more than once. It can be either a function on one variable or :ignore or :force. If it is :ignore, then the previously added edge is returned; if it is :force, then another edge is added between the two vertexes; if it is a function, then this function will be called with the previous edge.

Delete the edge' from the graph' and returns it.

Delete all edges from `graph'. Returns the graph..

Finds an edge in the graph between the two specified vertexes. If values (i.e., non-vertexes) are passed in, then the graph will be searched for matching vertexes.

Remove a vertex from a graph. The 'vertex-or-value' argument can be a vertex of the graph or a 'value' that will find a vertex via a call to find-vertex. A graph-vertex-not-found-error will be raised if the vertex is not found or is not part of the graph.

Replace vertex old in graph graph with vertex new. The edge structure of the graph is maintained.

Attaches the edge edge to the vertex vertex.

Make-vertex-container is called during graph creation and can be used to create specialized containers to hold graph vertexes.

Make-edge-container is called during graph creation and can be used to create specialized containers to hold graph edges.

It should not usually necessary to call this in user code. Creates a new edge between vertex-1 and vertex-2 for the graph. If the edge-type and edge-class are not specified, they will be determined from the defaults of the graph.

Creates a new vertex for graph graph. The keyword arguments include:

• vertex-class : specify the class of the vertex
• element : specify the element of the vertex

and any other initialization arguments that make sense for the vertex class.

Create a new graph given a list of vertexes (which are assumed to be from the same graph). The new graph contains all of the vertexes in the list and all of the edges between any vertexes on the list.

Returns the number of edges attached to vertex. Compare with the more flexible vertex-degree.

Returns the number of vertexes in graph. [?? could be a defun]

Returns the number of source edges of vertex (cf. source-edges). [?? could be a defun]

Returns the number of target edges of vertex (cf. target-edges). [?? could be a defun]

Returns the number of neighbors of vertex (cf. neighbor-vertexes). [?? could be a defun]

In a directed graph, returns true if vertex has any edges that point from vertex to some other vertex (cf. iterate-target-edges). In an undirected graph, has-children-p is testing only whether or not the vertex has any edges.

In a directed graph, returns true if vertex has any edges that point from some other vertex to this vertex (cf. iterate-source-edges). In an undirected graph, has-parent-p is testing only whether or not the vertex has any edges.

Returns the source-vertex of a directed edge. Compare with vertex-1.

Returns the target-vertex of a directed edge. Compare with vertex-2.

Returns true if-and-only-if edge is undirected

Returns true if-and-only-if edge is directed

Called during the initialization of a vertex to create the create the container used to store the edges incident to the vertex. The initarg :vertex-edges-container-class can be used to alter the default container class.

Assuming that the value-or-vertex corresponds to one of the vertexes for edge, this method returns the other vertex of edge. If the value-or-vertex is not part of edge, then an error is signaled. [?? Should create a new condition for this]

Return true if vertex-1 and vertex-2 are connected by an edge. [?? Compare adjacentp]

Returns true if the edge is connected to vertex and is either an undirected edge or a directed edge for which vertex is the source vertex of the edge.

Return true if-and-only-if an undirected cycle in graph is reachable from start-vertex.

Return true if vertex-1 and vertex-2 are connected by an edge. [?? compare with vertices-share-edge-p and remove one or maybe call one directed-adjacentp]

Returns the maximum depth of the vertexes in graph assuming that the roots are of depth 0 and that each edge distance from the roots increments the depth by one.

Returns true if the weight of edge-1 is strictly less than the weight of edge-2.

Returns true if and only if edge-1 is undirected and edge-2 is directed.

Returns the weight of an edge. This defaults to 1.0 and can only be altered if the edge is a sub-class of weighted-edge-mixin.

Returns true if vertex is a root vertex (i.e., it has no incoming (source) edges).

Returns true if start-vertex is in some cycle in graph. This uses child-vertexes to generate the vertexes adjacent to a vertex.

Returns true if there are any undirected cycles in graph.

Search 'graph' for a vertex with element 'value'. The search is fast but inflexible because it uses an associative-container. If you need more flexibity, see search-for-vertex.

Search 'graph' for a vertex with element 'value'. The 'key' function is applied to each element before that element is compared with the value. The comparison is done using the function 'test'. If you don't need to use key or test, then consider using find-vertex instead.

Search graph for an edge whose vertexes match edge. This means that vertex-1 of the edge in the graph must match vertex-1 of edge and so forth. Wil signal an error of type graph-edge-not-found-error unless error-if-not-found? is nil. [?? Unused. Remove?]

Searches graph for an edge that connects vertex-1 and vertex-2. [?? Ignores error-if-not-found? Does directedness matter? need test]

Returns the first vertex in thing for which the predicate function returns non-nil. If the key is supplied, then it is applied to the vertex before the predicate is.

Returns the first edge in thing for which the predicate function returns non-nil. If the key is supplied, then it is applied to the edge before the predicate is.

Returns a list of edges in thing for which the predicate returns non-nil. [?? why no key function?]

Returns a list of vertexes in thing for which the predicate returns non-nil. [?? why no key function?]

Finds and returns an edge between value-or-vertex-1 and value-or-vertex-2 which returns true (as a generalized boolean) when evaluated by fn. Unless error-if-not-found? is nil, then a error will be signaled. [?? IS error really signaled? need a test.]

Returns a union-find-container representing the connected-components of graph.

Returns the number of connected-components of graph.

Returns a list of sub-graphs of graph where each sub-graph is a different connected component of graph. Compare with connected-components and connected-component-count.

Returns true if graph is a connected graph and nil otherwise.

Returns a minimum spanning tree of graph if one exists and nil otherwise.

Returns a version of graph which is a directed free tree rooted at root.

Creates the unimodal bipartite projects of existing-graph with vertexes for each vertex of existing graph whose vertex-classifier is eq to vertex-class and where an edge existing between two vertexes of the graph if and only if they are connected to a shared vertex in the existing-graph.

WIP

WIP

Returns a list of the roots of graph. A root is defined as a vertex with no source edges (i.e., all of the edges are out-going). (cf. rootp) [?? could be a defun]

Returns a list of vertexes sorted by the depth from the roots of the graph. See also assign-level and graph-roots.

Sets the depth of vertex to level and then recursively sets the depth of all of the children of vertex to (1+ level).

Calls fn on every child of node.

Calls fn on every vertex that is either connected to vertex by an undirected edge or is at the source end of a directed edge.

Calls fn on every vertex adjecent to vertex See also iterate-children and iterate-parents.

Calls fn on each edge of graph or vertex.

In a directed graph, calls fn on each edge of a vertex that begins at vertex. In an undirected graph, this is equivalent to iterate-edges.

In a directed graph, calls fn on each edge of a vertex that ends at vertex. In an undirected graph, this is equivalent to iterate-edges.

Returns a list of the source edges of vertex. I.e., the edges that begin at vertex.

Returns a list of the target edges of vertex. I.e., the edges that end at vertex.

Returns a list of the vertexes to which vertex is connected by an edge and for which vertex is the source vertex. If the connecting edge is undirected, then the vertex is always counted as a source. [?? Could be a defun].

Returns a list of the vertexes to which vertex is connected by an edge and for which vertex is the target vertex. If the connecting edge is undirected, then the vertex is always counted as a target. [?? Could be a defun].

Returns a list of the vertexes to which vertex is connected by an edge disregarding edge direction. In a directed graph, neighbor-vertexes is the union of parent-vertexes and child-vertexes. [?? Could be a defun].

Calls fn on each of the vertexes of thing.

Returns a list of the edges of thing.

Returns a list of the vertexes of thing.

Generates a description of graph in DOT file format. The formatting can be altered using graph->dot-properties, vertex->dot, and edge->dot as well as edge-formatter, vertex-formatter, vertex-labeler, and edge-labeler. These can be specified directly in the call to graph->dot or by creating subclasses of basic-graph, basic-vertex and basic-edge.

The output can be a stream or pathname or one of the values nil or t. If output is nil, then graph->dot returns a string containing the DOT description. If it is t, then the DOT description is written to *standard-output*.

Here is an example;

(let ((g (make-container 'graph-container :default-edge-type :directed)))  
  (loop for (a b) in '((a b) (b c) (b d) (d e) (e f) (d f)) do  
        (add-edge-between-vertexes g a b))  
  (graph->dot g nil))  
 
"digraph G {  
E []  
C []  
B []  
A []  
D []  
F []  
E->F []  
B->C []  
B->D []  
A->B []  
D->E []  
D->F []  
}" 

For more information about DOT file format, search the web for 'DOTTY' and 'GRAPHVIZ'.

Unless a different graph-formatter is specified, this method is called by graph->dot to output graph-properties onto a stream. The function can assume that the openning and closing brackets will be taken care of by the graph->dot.

Unless a different vertex-formatter is specified with a keyword argument, this is used by graph->dot to output vertex formatting for vertex onto the stream. The function can assume that openning and closing square brackets and label have already been taken care of.

Used by graph->dot to output edge formatting for edge onto the stream. The function can assume that openning and closing square brackets and label have already been taken care of.

Generate an external represenation of a graph to a file, by running the program in dot-path.

Ensures that the graph is undirected (possibly by calling change-class on the edges).

Assign a number to each vertex in a graph in some unspecified order. [?? internal]

Assign a number to each edge in a graph in some unspecified order. [?? internal]

Add edges between vertexes in the new-graph for which the matching vertexes in the old-graph have edges. The vertex matching is done using find-vertex.

Returns a new graph that is a subset of graph that contains vertex and all of the other vertexes that can be reached from vertex by paths of less than or equal of length depth. If depth is not specified, then the entire sub-graph reachable from vertex will be returned. [?? Edge weights are always assumed to be one.]

Takes a GRAPH and a TEST-FN (a single argument function returning NIL or non-NIL), and filters the graph nodes according to the test-fn (those that return non-NIL are accepted), returning a new graph with only nodes corresponding to those in the original graph that satisfy the test (the nodes in the new graph are new, but their values and name point to the same contents of the original graph). There are four options for how the new graph is filled-out, depending on the following keywords passed to the optional GRAPH-COMPLETION-METHOD argument:

• NIL (default)

  New graph has only nodes that correspond to those in the original graph that pass the test. NO LINKS are reproduced.

• :COMPLETE-LINKS

  New graph has only nodes that pass, but reproduces corresponding links between passing nodes in the original graph.

• :COMPLETE-CLOSURE-NODES-ONLY

  New graph also includes nodes corresponding to the transitive closure(s) that include the passign nodes in the original graph. NO LINKS are reproduced.

• :COMPLETE-CLOSURE-WITH-LINKS

  Same as above, except corresponding links are reproduced.

For both transitive closure options, an additional optional argument, DEPTH, specifies how many links away from a source vertex to travel in gathering vertexes of the closure. E.g., a depth of 1 returns the source vertex and the parents and children of that vertex (all vertexes one link away from the source). The default value is NIL, indicating that all vertexes are to be included, no matter their depth. This value is ignored in non closure options.

Sets the tag of all the edges of thing to true. [?? why does this exist?]

Sets the tag of all the edges of thing to true. [?? why does this exist?]

Sets the tag of all the edges of thing to true. [?? why does this exist?]

Sets the tag of all the edges of thing to nil. [?? why does this exist?]

Returns true if-and-only-if edge's tag slot is t

Returns true if-and-only-if edge's tage slot is nil