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-rw-r--r--lib/stdlib/doc/src/digraph_utils.xml170
1 files changed, 55 insertions, 115 deletions
diff --git a/lib/stdlib/doc/src/digraph_utils.xml b/lib/stdlib/doc/src/digraph_utils.xml
index 4b137456b3..e44632bfd2 100644
--- a/lib/stdlib/doc/src/digraph_utils.xml
+++ b/lib/stdlib/doc/src/digraph_utils.xml
@@ -4,7 +4,7 @@
<erlref>
<header>
<copyright>
- <year>2000</year><year>2009</year>
+ <year>2000</year><year>2011</year>
<holder>Ericsson AB. All Rights Reserved.</holder>
</copyright>
<legalnotice>
@@ -119,49 +119,43 @@
considering all edges undirected.</p>
</description>
+ <datatypes>
+ <datatype>
+ <name><marker id="type-digraph">digraph()</marker></name>
+ <desc><p>A digraph as returned by <c>digraph:new/0,1</c>.</p></desc>
+ </datatype>
+ </datatypes>
<funcs>
<func>
- <name>arborescence_root(Digraph) -> no | {yes, Root}</name>
+ <name name="arborescence_root" arity="1"/>
<fsummary>Check if a digraph is an arborescence.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Root = vertex()</v>
- </type>
<desc>
-
- <p>Returns <c>{yes, Root}</c> if <c>Root</c> is
+ <p>Returns <c>{yes, <anno>Root</anno>}</c> if <c><anno>Root</anno></c> is
the <seealso marker="#root">root</seealso> of the arborescence
- <c>Digraph</c>, <c>no</c> otherwise.
+ <c><anno>Digraph</anno></c>, <c>no</c> otherwise.
</p>
</desc>
</func>
<func>
- <name>components(Digraph) -> [Component]</name>
+ <name name="components" arity="1"/>
<fsummary>Return the components of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Component = [vertex()]</v>
- </type>
<desc>
<p>Returns a list
of <seealso marker="#components">connected components</seealso>.
Each component is represented by its
vertices. The order of the vertices and the order of the
components are arbitrary. Each vertex of the digraph
- <c>Digraph</c> occurs in exactly one component.
+ <c><anno>Digraph</anno></c> occurs in exactly one component.
</p>
</desc>
</func>
<func>
- <name>condensation(Digraph) -> CondensedDigraph</name>
+ <name name="condensation" arity="1"/>
<fsummary>Return a condensed graph of a digraph.</fsummary>
- <type>
- <v>Digraph = CondensedDigraph = digraph()</v>
- </type>
<desc>
<p>Creates a digraph where the vertices are
the <seealso marker="#strong_components">strongly connected
- components</seealso> of <c>Digraph</c> as returned by
+ components</seealso> of <c><anno>Digraph</anno></c> as returned by
<c>strong_components/1</c>. If X and Y are strongly
connected components, and there exist vertices x and y in X
and Y respectively such that there is an
@@ -169,7 +163,7 @@
and <seealso marker="#incident">incident</seealso> on y, then
an edge emanating from X and incident on Y is created.
</p>
- <p>The created digraph has the same type as <c>Digraph</c>.
+ <p>The created digraph has the same type as <c><anno>Digraph</anno></c>.
All vertices and edges have the
default <seealso marker="#label">label</seealso> <c>[]</c>.
</p>
@@ -181,12 +175,8 @@
</desc>
</func>
<func>
- <name>cyclic_strong_components(Digraph) -> [StrongComponent]</name>
+ <name name="cyclic_strong_components" arity="1"/>
<fsummary>Return the cyclic strong components of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>StrongComponent = [vertex()]</v>
- </type>
<desc>
<p>Returns a list of <seealso marker="#strong_components">strongly
connected components</seealso>.
@@ -194,67 +184,50 @@
by its vertices. The order of the vertices and the order of
the components are arbitrary. Only vertices that are
included in some <seealso marker="#cycle">cycle</seealso> in
- <c>Digraph</c> are returned, otherwise the returned list is
+ <c><anno>Digraph</anno></c> are returned, otherwise the returned list is
equal to that returned by <c>strong_components/1</c>.
</p>
</desc>
</func>
<func>
- <name>is_acyclic(Digraph) -> bool()</name>
+ <name name="is_acyclic" arity="1"/>
<fsummary>Check if a digraph is acyclic.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- </type>
<desc>
<p>Returns <c>true</c> if and only if the digraph
- <c>Digraph</c> is <seealso marker="#acyclic_digraph">acyclic</seealso>.</p>
+ <c><anno>Digraph</anno></c> is <seealso marker="#acyclic_digraph">acyclic</seealso>.</p>
</desc>
</func>
<func>
- <name>is_arborescence(Digraph) -> bool()</name>
+ <name name="is_arborescence" arity="1"/>
<fsummary>Check if a digraph is an arborescence.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- </type>
<desc>
<p>Returns <c>true</c> if and only if the digraph
- <c>Digraph</c> is
+ <c><anno>Digraph</anno></c> is
an <seealso marker="#arborescence">arborescence</seealso>.</p>
</desc>
</func>
<func>
- <name>is_tree(Digraph) -> bool()</name>
+ <name name="is_tree" arity="1"/>
<fsummary>Check if a digraph is a tree.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- </type>
<desc>
<p>Returns <c>true</c> if and only if the digraph
- <c>Digraph</c> is
+ <c><anno>Digraph</anno></c> is
a <seealso marker="#tree">tree</seealso>.</p>
</desc>
</func>
<func>
- <name>loop_vertices(Digraph) -> Vertices</name>
+ <name name="loop_vertices" arity="1"/>
<fsummary>Return the vertices of a digraph included in some loop.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
- <p>Returns a list of all vertices of <c>Digraph</c> that are
+ <p>Returns a list of all vertices of <c><anno>Digraph</anno></c> that are
included in some <seealso marker="#loop">loop</seealso>.</p>
</desc>
</func>
<func>
- <name>postorder(Digraph) -> Vertices</name>
+ <name name="postorder" arity="1"/>
<fsummary>Return the vertices of a digraph in post-order.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
- <p>Returns all vertices of the digraph <c>Digraph</c>. The
+ <p>Returns all vertices of the digraph <c><anno>Digraph</anno></c>. The
order is given by
a <seealso marker="#depth_first_traversal">depth-first
traversal</seealso> of the digraph, collecting visited
@@ -266,14 +239,10 @@
</desc>
</func>
<func>
- <name>preorder(Digraph) -> Vertices</name>
+ <name name="preorder" arity="1"/>
<fsummary>Return the vertices of a digraph in pre-order.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
- <p>Returns all vertices of the digraph <c>Digraph</c>. The
+ <p>Returns all vertices of the digraph <c><anno>Digraph</anno></c>. The
order is given by
a <seealso marker="#depth_first_traversal">depth-first
traversal</seealso> of the digraph, collecting visited
@@ -281,119 +250,94 @@
</desc>
</func>
<func>
- <name>reachable(Vertices, Digraph) -> Vertices</name>
+ <name name="reachable" arity="2"/>
<fsummary>Return the vertices reachable from some vertices of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
<p>Returns an unsorted list of digraph vertices such that for
each vertex in the list, there is
- a <seealso marker="#path">path</seealso> in <c>Digraph</c> from some
- vertex of <c>Vertices</c> to the vertex. In particular,
+ a <seealso marker="#path">path</seealso> in <c><anno>Digraph</anno></c> from some
+ vertex of <c><anno>Vertices</anno></c> to the vertex. In particular,
since paths may have length zero, the vertices of
- <c>Vertices</c> are included in the returned list.
+ <c><anno>Vertices</anno></c> are included in the returned list.
</p>
</desc>
</func>
<func>
- <name>reachable_neighbours(Vertices, Digraph) -> Vertices</name>
+ <name name="reachable_neighbours" arity="2"/>
<fsummary>Return the neighbours reachable from some vertices of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
<p>Returns an unsorted list of digraph vertices such that for
each vertex in the list, there is
- a <seealso marker="#path">path</seealso> in <c>Digraph</c> of length
- one or more from some vertex of <c>Vertices</c> to the
+ a <seealso marker="#path">path</seealso> in <c><anno>Digraph</anno></c> of length
+ one or more from some vertex of <c><anno>Vertices</anno></c> to the
vertex. As a consequence, only those vertices
- of <c>Vertices</c> that are included in
+ of <c><anno>Vertices</anno></c> that are included in
some <seealso marker="#cycle">cycle</seealso> are returned.
</p>
</desc>
</func>
<func>
- <name>reaching(Vertices, Digraph) -> Vertices</name>
+ <name name="reaching" arity="2"/>
<fsummary>Return the vertices that reach some vertices of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
<p>Returns an unsorted list of digraph vertices such that for
each vertex in the list, there is
a <seealso marker="#path">path</seealso> from the vertex to some
- vertex of <c>Vertices</c>. In particular, since paths may have
- length zero, the vertices of <c>Vertices</c> are included in
+ vertex of <c><anno>Vertices</anno></c>. In particular, since paths may have
+ length zero, the vertices of <c><anno>Vertices</anno></c> are included in
the returned list.
</p>
</desc>
</func>
<func>
- <name>reaching_neighbours(Vertices, Digraph) -> Vertices</name>
+ <name name="reaching_neighbours" arity="2"/>
<fsummary>Return the neighbours that reach some vertices of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
<p>Returns an unsorted list of digraph vertices such that for
each vertex in the list, there is
a <seealso marker="#path">path</seealso> of length one or more
- from the vertex to some vertex of <c>Vertices</c>. As a consequence,
- only those vertices of <c>Vertices</c> that are included in
+ from the vertex to some vertex of <c><anno>Vertices</anno></c>. As a consequence,
+ only those vertices of <c><anno>Vertices</anno></c> that are included in
some <seealso marker="#cycle">cycle</seealso> are returned.
</p>
</desc>
</func>
<func>
- <name>strong_components(Digraph) -> [StrongComponent]</name>
+ <name name="strong_components" arity="1"/>
<fsummary>Return the strong components of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>StrongComponent = [vertex()]</v>
- </type>
<desc>
<p>Returns a list of <seealso marker="#strong_components">strongly
connected components</seealso>.
Each strongly component is represented
by its vertices. The order of the vertices and the order of
the components are arbitrary. Each vertex of the digraph
- <c>Digraph</c> occurs in exactly one strong component.
+ <c><anno>Digraph</anno></c> occurs in exactly one strong component.
</p>
</desc>
</func>
<func>
- <name>subgraph(Digraph, Vertices [, Options]) -> Subgraph</name>
+ <name name="subgraph" arity="2"/>
+ <name name="subgraph" arity="3"/>
<fsummary>Return a subgraph of a digraph.</fsummary>
- <type>
- <v>Digraph = Subgraph = digraph()</v>
- <v>Options = [{type, SubgraphType}, {keep_labels, bool()}]</v>
- <v>SubgraphType = inherit | type()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
<p>Creates a maximal <seealso marker="#subgraph">subgraph</seealso> of <c>Digraph</c> having
- as vertices those vertices of <c>Digraph</c> that are
- mentioned in <c>Vertices</c>.
+ as vertices those vertices of <c><anno>Digraph</anno></c> that are
+ mentioned in <c><anno>Vertices</anno></c>.
</p>
<p>If the value of the option <c>type</c> is <c>inherit</c>,
- which is the default, then the type of <c>Digraph</c> is used
+ which is the default, then the type of <c><anno>Digraph</anno></c> is used
for the subgraph as well. Otherwise the option value of <c>type</c>
is used as argument to <c>digraph:new/1</c>.
</p>
<p>If the value of the option <c>keep_labels</c> is <c>true</c>,
which is the default, then
the <seealso marker="#label">labels</seealso> of vertices and edges
- of <c>Digraph</c> are used for the subgraph as well. If the value
+ of <c><anno>Digraph</anno></c> are used for the subgraph as well. If the value
is <c>false</c>, then the default label, <c>[]</c>, is used
for the subgraph's vertices and edges.
</p>
- <p><c>subgraph(Digraph, Vertices)</c> is equivalent to
- <c>subgraph(Digraph, Vertices, [])</c>.
+ <p><c>subgraph(<anno>Digraph</anno>, <anno>Vertices</anno>)</c> is equivalent to
+ <c>subgraph(<anno>Digraph</anno>, <anno>Vertices</anno>, [])</c>.
</p>
<p>There will be a <c>badarg</c> exception if any of the arguments
are invalid.
@@ -401,16 +345,12 @@
</desc>
</func>
<func>
- <name>topsort(Digraph) -> Vertices | false</name>
+ <name name="topsort" arity="1"/>
<fsummary>Return a topological sorting of the vertices of a digraph.</fsummary>
- <type>
- <v>Digraph = digraph()</v>
- <v>Vertices = [vertex()]</v>
- </type>
<desc>
<p>Returns a <seealso marker="#topsort">topological
ordering</seealso> of the vertices of the digraph
- <c>Digraph</c> if such an ordering exists, <c>false</c>
+ <c><anno>Digraph</anno></c> if such an ordering exists, <c>false</c>
otherwise. For each vertex in the returned list, there are
no <seealso marker="#out_neighbour">out-neighbours</seealso>
that occur earlier in the list.</p>
generated by cgit v1.2.3 (git 2.25.1) at 2024-07-01 16:09:21 +0000