File size: 29,081 Bytes

43203b4

(in-package #:cl-graph)


(defgeneric make-vertex-container (graph initial-size)
  (:documentation "Make-vertex-container is called during graph
  creation and can be used to create specialized containers to hold
  graph vertexes."))


(defgeneric make-edge-container (graph initial-size)
  (:documentation "Make-edge-container is called during graph creation
  and can be used to create specialized containers to hold graph
  edges."))

;;; API

(defgeneric make-graph (graph-type &key &allow-other-keys)
  (:documentation "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."))


(defgeneric make-edge-for-graph (graph vertex-1 vertex-2
                                       &key edge-type edge-class
				       &allow-other-keys)
  (:documentation "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."))


(defgeneric add-edge (graph edge &rest args &key force-new?)
  (:documentation "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."))


(defgeneric add-edge-between-vertexes (graph value-or-vertex-1 value-or-vertex-2
                                              &rest args &key if-duplicate-do
                                              edge-type &allow-other-keys)
  (:documentation "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."))


(defgeneric delete-edge (graph edge)
  (:documentation "Delete the `edge' from the `graph' and returns it."))

(defgeneric delete-all-edges (graph)
  (:documentation "Delete all edges from `graph'. Returns the graph.."))


(defgeneric delete-edge-between-vertexes (graph value-or-vertex-1
                                                value-or-vertex-2 &rest args)
  (:documentation "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."))


(defgeneric add-vertex (graph value-or-vertex &key if-duplicate-do &allow-other-keys)
  (:documentation "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."))


(defgeneric delete-vertex (graph value-or-vertex)
  (:documentation "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."))


(defgeneric find-vertex (graph value &optional error-if-not-found?)
  (:documentation "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."))


(defgeneric search-for-vertex (graph value &key key test error-if-not-found?)
  (:documentation "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."))


(defgeneric find-edge (graph edge &optional error-if-not-found?)
  (:documentation "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?]"))


(defgeneric find-edge-between-vertexes (graph value-or-vertex-1 value-or-vertex-2
                                              &key error-if-not-found?)
  (:documentation "Searches `graph` for an edge that connects vertex-1
  and vertex-2.  [?? Ignores error-if-not-found? Does directedness
  matter? need test]"))


(defgeneric source-vertex (edge)
  (:documentation "Returns the source-vertex of a directed
  edge. Compare with `vertex-1`."))


(defgeneric target-vertex (edge)
  (:documentation "Returns the target-vertex of a directed
  edge. Compare with `vertex-2`."))


(defgeneric iterate-edges (graph-or-vertex fn)
  (:documentation "Calls `fn` on each edge of graph or vertex."))


(defgeneric iterate-source-edges (vertex fn)
  (:documentation "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`."))


(defgeneric iterate-target-edges (vertex fn)
  (:documentation "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`."))

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


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


(defgeneric iterate-parents (vertex fn)
  (:documentation "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."))


(defgeneric iterate-neighbors (vertex fn)
  (:documentation "Calls fn on every vertex adjecent to vertex See
  also iterate-children and iterate-parents."))


(defgeneric renumber-vertexes (graph)
  (:documentation "Assign a number to each vertex in a graph in some
  unspecified order. [?? internal]"))


(defgeneric renumber-edges (graph)
  (:documentation "Assign a number to each edge in a graph in some
  unspecified order. [?? internal]"))


(defgeneric generate-directed-free-tree (graph root)
  (:documentation "Returns a version of graph which is a directed free
tree rooted at root."))


(defgeneric in-undirected-cycle-p (graph start-vertex &optional marked previous)
  (:documentation "Return true if-and-only-if an undirected cycle in
  graph is reachable from start-vertex."))


(defgeneric undirected-edge-p (edge)
  (:documentation "Returns true if-and-only-if edge is undirected"))


(defgeneric directed-edge-p (edge)
  (:documentation "Returns true if-and-only-if edge is directed"))


(defgeneric tagged-edge-p (edge)
  (:documentation "Returns true if-and-only-if edge's tag slot is t"))


(defgeneric untagged-edge-p (edge)
  (:documentation "Returns true if-and-only-if edge's tage slot is nil"))


(defgeneric adjacentp (graph vertex-1 vertex-2)
  (:documentation "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]"))


(defgeneric make-filtered-graph (old-graph test-fn &key
					   graph-completion-method depth
					   new-graph)
  (:documentation "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."))


(defgeneric project-bipartite-graph
  (new-graph existing-graph vertex-class vertex-classifier)
  (:documentation "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."))


(defgeneric assortativity-coefficient (mixing-matrix)
  (:documentation "An assortative graph is one where vertexes of the
same type are more likely to have edges between them. The \(discrete\)
assortativity-coefficient measures how assortative a graph is based on
its mixing matrix. The definition we use is from Mixing Patterns in
Networks by Mark Newman. See the citation 'newman200-mixing' in moab
or the URL 'http://arxiv.org/abs/cond-mat/0209450'."))


(defgeneric graph->dot (graph output
                       &key
                       graph-formatter
                       vertex-key
                       vertex-labeler
                       vertex-formatter
                       edge-labeler
                       edge-formatter)
  (:documentation
   "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'."))


(defgeneric graph->dot-properties (g stream)
  (:documentation "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."))


(defgeneric vertex->dot (vertex stream)
  (:documentation "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."))


(defgeneric edge->dot (edge stream)
  (:documentation "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."))


(defgeneric generate-gnm (generator graph n m &key)
  (:documentation "Generate a 'classic' random graph G(n, m) with n
  vertexes and m edges."))


(defgeneric generate-gnp (generator graph n p &key)
  (:documentation "Generate the Erd\"os-R\'enyi random graph G\(n,
p\). I.e., a graph with n vertexes where each possible edge appears
with probability p. This implementation is from Efficient Generation
of Large Random Networks \(see batagelj-generation-2005 in doab\)."))


(defgeneric generate-undirected-graph-via-assortativity-matrix
  (generator graph-class size edge-count kind-matrix assortativity-matrix
             vertex-labeler &key)
  (:documentation "This generates a random graph with 'size' vertexes.
The vertexes can be in multiple different classes and the number of
vertexes in each class is specified in the 'kind-matrix'. If the
matrix has all fixnums, then it specifies the counts and these should
add up to the size. If the kind-matrix contains non-fixnums then the
values are treated as ratios.

The assortativity-matrix specifies the number of edges between
vertexes of different kinds.

The vertex-labeler is a function of two parameters: the vertex kind
and the index. It should return whatever the 'value' of the vertex
ought to be."))


(defgeneric generate-undirected-graph-via-vertex-probabilities
  (generator graph-class size kind-matrix probability-matrix vertex-labeler)
  (:documentation "Generate an Erd\"os-R/'enyi like random graph
having multiple vertex kinds. See the function Gnp for the simple one
vertex kind method.

Generator and graph-class specify the random number generator used and
the class of the graph produced; Size the number of vertexes. Kind
matrix is a vector of ratios specifying the distribution of vertex
kinds {0 ... \(1- k\)}.  The probability-matrix is a k x k matrix
specifying the probability that two vertexes of the row-kind and the
column-kind will have an edge between them. vertex-labeler is a
function of two arguments \(the kind and the vertex number\) called to
create values for vertexes. It will be called only once for each
vertex created.

The clever sequential sampling technique in this implementation is
from Efficient Generation of Large Random Networks \(see
batagelj-generation-2005 in moab\)."))


(defgeneric generate-scale-free-graph
  (generator graph size kind-matrix add-edge-count
             other-vertex-kind-samplers vertex-labeler &key)
  (:documentation "Generates a 'scale-free' graph using preferential
  attachment -- too damn slow.

Size is the number of vertexes; kind-matrix is as in
generate-undirected-graph-via-assortativity-matrix, etc.;
add-edge-count is the number of edges to add for each vertex;
other-vertex-kind-samplers are confusing...; and vertex-labeler is
used to create vertex elements \(as in other generators\)."))


(defgeneric generate-assortative-graph-with-degree-distributions
  (generator graph
             edge-count assortativity-matrix
             average-degrees
             degree-distributions
             vertex-labeler
             &key)
  (:documentation ""))


(defgeneric generate-simple-preferential-attachment-graph (generator graph size minimum-degree)
  (:documentation "Generate a simple scale-free graph using the
preferential attachment mechanism of Barabasi and Albert. The
implementation is from Efficient Generation of Large Random Networks
\(see batagelj-generation-2005 in moab\). Self-edges are possible."))


(defgeneric generate-preferential-attachment-graph
  (generator graph size kind-matrix minimum-degree
             assortativity-matrix
             &key)
  (:documentation "Generate a Barabasi-Albert type scale free graph
  with multiple vertex kinds.

The idea behind this implementation is from Efficient Generation of
Large Random Networks \(see batagelj-generation-2005 in moab\)."))


;;; more

(defgeneric make-vertex-for-graph (graph &key &allow-other-keys)
  (:documentation "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."))


(defgeneric tag-all-edges (thing)
  (:documentation "Sets the `tag` of all the edges of `thing` to
  true. [?? why does this exist?\]"))


(defgeneric untag-all-edges (thing)
  (:documentation "Sets the `tag` of all the edges of `thing` to nil.
  [?? why does this exist?\]"))


(defgeneric untag-edges (edges)
  (:documentation "Sets the `tag` of all the edges of `thing` to
  true. [?? why does this exist?\]"))


(defgeneric tag-edges (edges)
  (:documentation "Sets the `tag` of all the edges of `thing` to
  true. [?? why does this exist?\]"))


(defgeneric replace-vertex (graph old new)
  (:documentation "Replace vertex `old` in graph `graph` with vertex
  `new`. The edge structure of the graph is maintained."))


(defgeneric add-edge-to-vertex (edge vertex)
  (:documentation "Attaches the edge `edge` to the vertex `vertex`."))


(defgeneric source-edges (vertex &optional filter)
  (:documentation "Returns a list of the source edges of
`vertex`. I.e., the edges that begin at `vertex`."))


(defgeneric target-edges (vertex &optional filter)
  (:documentation "Returns a list of the target edges of `vertex`.
I.e., the edges that end at `vertex`."))


(defgeneric child-vertexes (vertex &optional filter)
  (:documentation "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]."))


(defgeneric parent-vertexes (vertex &optional filter)
  (:documentation "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]."))


(defgeneric neighbor-vertexes (vertex &optional filter)
  (:documentation "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]."))


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


(defgeneric in-cycle-p (graph start-vertex)
  (:documentation "Returns true if `start-vertex` is in some cycle in
  `graph`. This uses child-vertexes to generate the vertexes adjacent
  to a vertex."))


(defgeneric iterate-vertexes (thing fn)
  (:documentation "Calls `fn` on each of the vertexes of `thing`."))


(defgeneric edges (thing)
  (:documentation "Returns a list of the edges of `thing`."))


(defgeneric vertex-count (graph)
  (:documentation "Returns the number of vertexes in `graph`. [??
  could be a defun]"))


(defgeneric vertexes (thing)
  (:documentation "Returns a list of the vertexes of `thing`."))


(defgeneric source-edge-count (vertex)
  (:documentation "Returns the number of source edges of
  vertex (cf. source-edges). [?? could be a defun]"))


(defgeneric target-edge-count (vertex)
  (:documentation "Returns the number of target edges of
  vertex (cf. target-edges). [?? could be a defun]"))


(defgeneric graph-roots (graph)
  (:documentation "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]"))


(defgeneric rootp (vertex)
  (:documentation "Returns true if `vertex` is a root vertex \(i.e.,
  it has no incoming \(source\) edges\)."))


(defgeneric find-vertex-if (thing predicate &key key)
  (:documentation "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."))


(defgeneric find-edge-if (graph fn &key key)
  (:documentation "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."))


(defgeneric find-edges-if (thing predicate)
  (:documentation "Returns a list of edges in `thing` for which the
  `predicate` returns non-nil. [?? why no key function?]"))


(defgeneric find-vertexes-if (thing predicate)
  (:documentation "Returns a list of vertexes in `thing` for which the `predicate` returns non-nil. [?? why no key function?]"))


(defgeneric force-undirected (graph)
  (:documentation "Ensures that the graph is undirected (possibly by
  calling change-class on the edges)."))


(defgeneric traverse-elements (thing style fn)
  (:documentation "WIP"))

(defgeneric traverse-elements-helper (thing style marker fn)
  (:documentation "WIP"))

(defgeneric any-undirected-cycle-p (graph)
  (:documentation "Returns true if there are any undirected cycles in `graph`."))

(defgeneric edge-count (vertex)
  (:documentation "Returns the number of edges attached to
  `vertex`. Compare with the more flexible `vertex-degree`."))

(defgeneric topological-sort (graph)
  (:documentation "Returns a list of vertexes sorted by the depth from
  the roots of the graph. See also assign-level and graph-roots."))

(defgeneric assign-level (vertex level)
  (:documentation "Sets the depth of `vertex` to level and then
  recursively sets the depth of all of the children of `vertex` to
  \(1+ level\)."))

(defgeneric depth (graph)
  (:documentation "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."))

(defgeneric make-vertex-edges-container (vertex container-class &rest args)
  (:documentation "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."))

(defgeneric other-vertex (edge value-or-vertex)
  (:documentation "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]"))

(defgeneric find-edge-between-vertexes-if
  (graph value-or-vertex-1 value-or-vertex-2 fn &key error-if-not-found?)
  (:documentation 
   "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.]"))

(defgeneric vertices-share-edge-p (vertex-1 vertex-2)
  (:documentation "Return true if vertex-1 and vertex-2 are connected
  by an edge. [?? Compare adjacentp]"))

(defgeneric graph-edge-mixture-matrix (graph vertex-classifier &key edge-weight)
  (:documentation "Return the `mixing-matrix` of graph based on the
  classifier and the edge-weight function. The mixing matrix is a
  matrix whose runs and columns represent each class of vertex in the
  graph. The entries of the matrix show the total number of edges
  between vertexes of the two kinds. [?? Edge-weight is not used; also
  compare with graph-mixture-matrix.]"))

(defgeneric graph-mixing-matrix (graph vertex-classifier &key edge-weight)
  (:documentation "Return the `mixing-matrix` of graph based on the
  classifier and the edge-weight function. The mixing matrix is a
  matrix whose runs and columns represent each class of vertex in the
  graph. The entries of the matrix show the total number of edges
  between vertexes of the two kinds. [?? Edge-weight is not used; also
  compare with graph-edge-mixture-matrix.]"))

(defgeneric connected-components (graph)
  (:documentation "Returns a union-find-container representing the
  connected-components of `graph`."))

(defgeneric connected-component-count (graph)
  (:documentation "Returns the number of connected-components of
  graph."))

(defgeneric find-connected-components (graph)
  (:documentation "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."))

(defgeneric initialize-vertex-data (graph)
  (:documentation ""))

(defgeneric breadth-first-visitor (graph source fn)
  (:documentation ""))

(defgeneric breadth-first-search-graph (graph source)
  (:documentation ""))

(defgeneric mst-find-set (vertex)
  (:documentation ""))

(defgeneric mst-make-set (vertex)
  (:documentation ""))

(defgeneric mst-tree-union (v1 v2)
  (:documentation ""))

(defgeneric mst-link (v1 v2)
  (:documentation ""))

(defgeneric add-edges-to-graph (graph edges &key if-duplicate-do)
  (:documentation ""))

(defgeneric make-graph-from-vertexes (vertex-list)
  (:documentation "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."))

(defgeneric edge-lessp-by-weight (edge-1 edge-2)
  (:documentation "Returns true if the weight of edge-1 is strictly less than the weight of edge-2."))

(defgeneric minimum-spanning-tree (graph &key edge-sorter)
  (:documentation "Returns a minimum spanning tree of graph if one exists and nil otherwise."))

(defgeneric connected-graph-p (graph &key edge-sorter)
  (:documentation "Returns true if graph is a connected graph and nil otherwise."))

(defgeneric edge-lessp-by-direction (edge-1 edge-2)
  (:documentation "Returns true if and only if edge-1 is undirected and edge-2 is directed."))

(defgeneric out-edge-for-vertex-p (edge vertex)
  (:documentation "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."))

(defgeneric dfs (graph root fn &key out-edge-sorter)
  (:documentation ""))

(defgeneric dfs-visit (graph u fn sorter)
  (:documentation ""))

(defgeneric dfs-tree-edge-p (edge)
  (:documentation ""))

(defgeneric dfs-back-edge-p (edge)
  (:documentation ""))

(defgeneric dfs-forward-edge-p (edge)
  (:documentation ""))

(defgeneric dfs-cross-edge-p (edge)
  (:documentation ""))

(defgeneric dfs-edge-type (edge)
  (:documentation ""))

(defgeneric map-over-all-combinations-of-k-vertexes (graph k fn)
  (:documentation ""))

(defgeneric map-over-all-combinations-of-k-edges (vertex k fn)
  (:documentation ""))

(defgeneric complete-links (new-graph old-graph)
  (:documentation "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`."))

(defgeneric subgraph-containing (graph vertex &key depth new-graph)
  (:documentation "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.]"))


(defgeneric weight (edge)
  (:documentation "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`."))

(defgeneric (setf dot-attribute-value) (value attribute thing)
  )

(defgeneric dot-attribute-value (attribute thing)
  )

(defgeneric graph->dot-external (graph file-name &key type)
  )

(defgeneric ensure-valid-dot-attribute (key object)
  )

(defgeneric write-name-for-dot (attribute stream)
  )