diff options
Diffstat (limited to 'lib/stdlib/doc/src/digraph.xml')
| -rw-r--r-- | lib/stdlib/doc/src/digraph.xml | 540 |
1 files changed, 298 insertions, 242 deletions
diff --git a/lib/stdlib/doc/src/digraph.xml b/lib/stdlib/doc/src/digraph.xml index 291be6c08b..5332d7aba5 100644 --- a/lib/stdlib/doc/src/digraph.xml +++ b/lib/stdlib/doc/src/digraph.xml @@ -4,7 +4,7 @@ <erlref> <header> <copyright> - <year>1996</year><year>2014</year> + <year>1996</year><year>2016</year> <holder>Ericsson AB. All Rights Reserved.</holder> </copyright> <legalnotice> @@ -30,64 +30,92 @@ <checked></checked> <date>2001-08-27</date> <rev>C</rev> - <file>digraph.sgml</file> + <file>digraph.xml</file> </header> <module>digraph</module> - <modulesummary>Directed Graphs</modulesummary> + <modulesummary>Directed graphs.</modulesummary> <description> - <p>The <c>digraph</c> module implements a version of labeled - directed graphs. What makes the graphs implemented here + <p>This module provides a version of labeled + directed graphs. What makes the graphs provided here non-proper directed graphs is that multiple edges between vertices are allowed. However, the customary definition of - directed graphs will be used in the text that follows. - </p> - <p>A <marker id="digraph"></marker><em>directed graph</em> (or just - "digraph") is a pair (V, E) of a finite set V of - <marker id="vertex"></marker><em>vertices</em> and a finite set E of - <marker id="edge"></marker><em>directed edges</em> (or just "edges"). - The set of - edges E is a subset of V × V (the Cartesian - product of V with itself). In this module, V is allowed to be - empty; the so obtained unique digraph is called the - <marker id="empty_digraph"></marker><em>empty digraph</em>. - Both vertices and edges are represented by unique Erlang terms. - </p> - <p>Digraphs can be annotated with additional information. Such - information may be attached to the vertices and to the edges of - the digraph. A digraph which has been annotated is called a - <em>labeled digraph</em>, and the information attached to a - vertex or an edge is called a <marker id="label"></marker> - <em>label</em>. Labels are Erlang terms. - </p> - <p>An edge e = (v, w) is said to - <marker id="emanate"></marker><em>emanate</em> from vertex v and - to be <marker id="incident"></marker><em>incident</em> on vertex w. - The <marker id="out_degree"></marker><em>out-degree</em> of a vertex - is the number of edges emanating from that vertex. - The <marker id="in_degree"></marker><em>in-degree</em> of a vertex - is the number of edges incident on that vertex. - If there is an edge emanating from v and incident on w, then w is - said to be an <marker id="out_neighbour"></marker> - <em>out-neighbour</em> of v, and v is said to be an - <marker id="in_neighbour"></marker><em>in-neighbour</em> of w. - A <marker id="path"></marker><em>path</em> P from v[1] to v[k] - in a digraph (V, E) is a non-empty sequence - v[1], v[2], ..., v[k] of vertices in V such that - there is an edge (v[i],v[i+1]) in E for - 1 <= i < k. - The <marker id="length"></marker><em>length</em> of the path P is k-1. - P is <marker id="simple_path"></marker><em>simple</em> if all - vertices are distinct, except that the first and the last vertices - may be the same. - P is a <marker id="cycle"></marker><em>cycle</em> if the length - of P is not zero and v[1] = v[k]. - A <marker id="loop"></marker><em>loop</em> is a cycle of length one. - A <marker id="simple_cycle"></marker><em>simple cycle</em> is a path - that is both a cycle and simple. - An <marker id="acyclic_digraph"></marker><em>acyclic digraph</em> - is a digraph that has no cycles. - </p> + directed graphs is used here.</p> + + <list type="bulleted"> + <item> + <p>A <marker id="digraph"></marker><em>directed graph</em> (or just + "digraph") is a pair (V, E) of a finite set V of + <marker id="vertex"></marker><em>vertices</em> and a finite set E of + <marker id="edge"></marker><em>directed edges</em> (or just "edges"). + The set of edges E is a subset of V × V (the + Cartesian product of V with itself).</p> + <p>In this module, V is allowed to be empty. The so obtained unique + digraph is called the + <marker id="empty_digraph"></marker><em>empty digraph</em>. Both + vertices and edges are represented by unique Erlang terms.</p> + </item> + <item> + <p>Digraphs can be annotated with more information. Such information + can be attached to the vertices and to the edges of the digraph. An + annotated digraph is called a <em>labeled digraph</em>, and the + information attached to a vertex or an edge is called a + <marker id="label"></marker><em>label</em>. Labels are Erlang + terms.</p> + </item> + <item> + <p>An edge e = (v, w) is said to + <marker id="emanate"></marker><em>emanate</em> from vertex v and to + be <marker id="incident"></marker><em>incident</em> on vertex w.</p> + </item> + <item> + <p>The <marker id="out_degree"></marker><em>out-degree</em> of a vertex + is the number of edges emanating from that vertex.</p> + </item> + <item> + <p>The <marker id="in_degree"></marker><em>in-degree</em> of a vertex + is the number of edges incident on that vertex.</p> + </item> + <item> + <p>If an edge is emanating from v and incident on w, then w is + said to be an <marker id="out_neighbour"></marker> + <em>out-neighbor</em> of v, and v is said to be an + <marker id="in_neighbour"></marker><em>in-neighbor</em> of w.</p> + </item> + <item> + <p>A <marker id="path"></marker><em>path</em> P from v[1] to v[k] + in a digraph (V, E) is a non-empty sequence + v[1], v[2], ..., v[k] of vertices in V such that + there is an edge (v[i],v[i+1]) in E for + 1 <= i < k.</p> + </item> + <item> + <p>The <marker id="length"></marker><em>length</em> of path P is + k-1.</p> + </item> + <item> + <p>Path P is <marker id="simple_path"></marker><em>simple</em> if all + vertices are distinct, except that the first and the last vertices + can be the same.</p> + </item> + <item> + <p>Path P is a <marker id="cycle"></marker><em>cycle</em> if the + length of P is not zero and v[1] = v[k].</p> + </item> + <item> + <p>A <marker id="loop"></marker><em>loop</em> is a cycle of length + one.</p> + </item> + <item> + <p>A <marker id="simple_cycle"></marker><em>simple cycle</em> is a path + that is both a cycle and simple.</p> + </item> + <item> + <p>An <marker id="acyclic_digraph"></marker><em>acyclic digraph</em> + is a digraph without cycles.</p> + </item> + </list> </description> + <datatypes> <datatype> <name name="d_type"/> @@ -100,20 +128,20 @@ </datatype> <datatype> <name name="graph"/> - <desc><p>A digraph as returned by <c>new/0,1</c>.</p></desc> + <desc><p>A digraph as returned by + <seealso marker="#new/0"><c>new/0,1</c></seealso>.</p></desc> </datatype> <datatype> <name>edge()</name> - <desc><p><marker id="type-edge"/></p></desc> </datatype> <datatype> <name name="label"/> </datatype> <datatype> <name>vertex()</name> - <desc><p><marker id="type-vertex"/></p></desc> </datatype> </datatypes> + <funcs> <func> <name name="add_edge" arity="3"/> @@ -122,291 +150,313 @@ <fsummary>Add an edge to a digraph.</fsummary> <type name="add_edge_err_rsn"/> <desc> - <p><c>add_edge/5</c> creates (or modifies) the edge <c><anno>E</anno></c> - of the digraph <c><anno>G</anno></c>, using <c><anno>Label</anno></c> as the (new) - <seealso marker="#label">label</seealso> of the edge. The + <p><c>add_edge/5</c> creates (or modifies) edge <c><anno>E</anno></c> + of digraph <c><anno>G</anno></c>, using <c><anno>Label</anno></c> as + the (new) <seealso marker="#label">label</seealso> of the edge. The edge is <seealso marker="#emanate">emanating</seealso> from - <c><anno>V1</anno></c> and <seealso marker="#incident">incident</seealso> - on <c><anno>V2</anno></c>. Returns <c><anno>E</anno></c>. - </p> - <p><c>add_edge(<anno>G</anno>, <anno>V1</anno>, <anno>V2</anno>, <anno>Label</anno>)</c> is - equivalent to + <c><anno>V1</anno></c> and + <seealso marker="#incident">incident</seealso> + on <c><anno>V2</anno></c>. Returns <c><anno>E</anno></c>.</p> + <p><c>add_edge(<anno>G</anno>, <anno>V1</anno>, <anno>V2</anno>, <anno>Label</anno>)</c> + is equivalent to <c>add_edge(<anno>G</anno>, <anno>E</anno>, <anno>V1</anno>, <anno>V2</anno>, <anno>Label</anno>)</c>, where <c><anno>E</anno></c> is a created edge. The created edge is - represented by the term <c>['$e' | N]</c>, where N - is an integer >= 0. - </p> - <p><c>add_edge(<anno>G</anno>, <anno>V1</anno>, <anno>V2</anno>)</c> is equivalent to + represented by term <c>['$e' | N]</c>, where <c>N</c> + is an integer >= 0.</p> + <p><c>add_edge(<anno>G</anno>, <anno>V1</anno>, <anno>V2</anno>)</c> + is equivalent to <c>add_edge(<anno>G</anno>, <anno>V1</anno>, <anno>V2</anno>, [])</c>. - </p> - <p>If the edge would create a cycle in - an <seealso marker="#acyclic_digraph">acyclic digraph</seealso>, - then <c>{error, {bad_edge, <anno>Path</anno>}}</c> is returned. If - either of <c><anno>V1</anno></c> or <c><anno>V2</anno></c> is not a vertex of the - digraph <c><anno>G</anno></c>, then + </p> + <p>If the edge would create a cycle in + an <seealso marker="#acyclic_digraph">acyclic digraph</seealso>, + <c>{error, {bad_edge, <anno>Path</anno>}}</c> is returned. + If either of <c><anno>V1</anno></c> or <c><anno>V2</anno></c> is not + a vertex of digraph <c><anno>G</anno></c>, <c>{error, {bad_vertex, </c><anno>V</anno><c>}}</c> is returned, <anno>V</anno> = <c><anno>V1</anno></c> or - <anno>V</anno> = <c><anno>V2</anno></c>. - </p> + <anno>V</anno> = <c><anno>V2</anno></c>.</p> </desc> </func> + <func> <name name="add_vertex" arity="1"/> <name name="add_vertex" arity="2"/> <name name="add_vertex" arity="3"/> <fsummary>Add or modify a vertex of a digraph.</fsummary> <desc> - <p><c>add_vertex/3</c> creates (or modifies) the vertex <c><anno>V</anno></c> - of the digraph <c><anno>G</anno></c>, using <c><anno>Label</anno></c> as the (new) + <p><c>add_vertex/3</c> creates (or modifies) vertex + <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>, using + <c><anno>Label</anno></c> as the (new) <seealso marker="#label">label</seealso> of the - vertex. Returns <c><anno>V</anno></c>. - </p> - <p><c>add_vertex(<anno>G</anno>, <anno>V</anno>)</c> is equivalent to - <c>add_vertex(<anno>G</anno>, <anno>V</anno>, [])</c>. - </p> + vertex. Returns <c><anno>V</anno></c>.</p> + <p><c>add_vertex(<anno>G</anno>, <anno>V</anno>)</c> is equivalent + to <c>add_vertex(<anno>G</anno>, <anno>V</anno>, [])</c>. + </p> <p><c>add_vertex/1</c> creates a vertex using the empty list as label, and returns the created vertex. The created vertex - is represented by the term <c>['$v' | N]</c>, - where N is an integer >= 0. - </p> + is represented by term <c>['$v' | N]</c>, + where <c>N</c> is an integer >= 0.</p> </desc> </func> + <func> <name name="del_edge" arity="2"/> <fsummary>Delete an edge from a digraph.</fsummary> <desc> - <p>Deletes the edge <c><anno>E</anno></c> from the digraph <c><anno>G</anno></c>. - </p> + <p>Deletes edge <c><anno>E</anno></c> from digraph + <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="del_edges" arity="2"/> <fsummary>Delete edges from a digraph.</fsummary> <desc> - <p>Deletes the edges in the list <c><anno>Edges</anno></c> from the digraph - <c><anno>G</anno></c>. - </p> + <p>Deletes the edges in list <c><anno>Edges</anno></c> from digraph + <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="del_path" arity="3"/> <fsummary>Delete paths from a digraph.</fsummary> <desc> - <p>Deletes edges from the digraph <c><anno>G</anno></c> until there are no - <seealso marker="#path">paths</seealso> from the vertex - <c><anno>V1</anno></c> to the vertex <c><anno>V2</anno></c>. - </p> - <p>A sketch of the procedure employed: Find an arbitrary - <seealso marker="#simple_path">simple path</seealso> - v[1], v[2], ..., v[k] from <c><anno>V1</anno></c> to - <c><anno>V2</anno></c> in <c><anno>G</anno></c>. Remove all edges of - <c><anno>G</anno></c> <seealso marker="#emanate">emanating</seealso> from v[i] - and <seealso marker="#incident">incident</seealso> to v[i+1] for - 1 <= i < k (including multiple - edges). Repeat until there is no path between <c><anno>V1</anno></c> and - <c><anno>V2</anno></c>. - </p> + <p>Deletes edges from digraph <c><anno>G</anno></c> until there are no + <seealso marker="#path">paths</seealso> from vertex + <c><anno>V1</anno></c> to vertex <c><anno>V2</anno></c>.</p> + <p>A sketch of the procedure employed:</p> + <list type="bulleted"> + <item> + <p>Find an arbitrary + <seealso marker="#simple_path">simple path</seealso> + v[1], v[2], ..., v[k] from <c><anno>V1</anno></c> + to <c><anno>V2</anno></c> in <c><anno>G</anno></c>.</p> + </item> + <item> + <p>Remove all edges of <c><anno>G</anno></c> + <seealso marker="#emanate">emanating</seealso> from v[i] and + <seealso marker="#incident">incident</seealso> to v[i+1] for + 1 <= i < k (including multiple + edges).</p> + </item> + <item> + <p>Repeat until there is no path between <c><anno>V1</anno></c> + and <c><anno>V2</anno></c>.</p> + </item> + </list> </desc> </func> + <func> <name name="del_vertex" arity="2"/> <fsummary>Delete a vertex from a digraph.</fsummary> <desc> - <p>Deletes the vertex <c><anno>V</anno></c> from the digraph <c><anno>G</anno></c>. Any - edges <seealso marker="#emanate">emanating</seealso> from - <c><anno>V</anno></c> or <seealso marker="#incident">incident</seealso> - on <c><anno>V</anno></c> are also deleted. - </p> + <p>Deletes vertex <c><anno>V</anno></c> from digraph + <c><anno>G</anno></c>. Any edges + <seealso marker="#emanate">emanating</seealso> from + <c><anno>V</anno></c> or + <seealso marker="#incident">incident</seealso> + on <c><anno>V</anno></c> are also deleted.</p> </desc> </func> + <func> <name name="del_vertices" arity="2"/> <fsummary>Delete vertices from a digraph.</fsummary> <desc> - <p>Deletes the vertices in the list <c><anno>Vertices</anno></c> from the - digraph <c><anno>G</anno></c>. - </p> + <p>Deletes the vertices in list <c><anno>Vertices</anno></c> from + digraph <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="delete" arity="1"/> <fsummary>Delete a digraph.</fsummary> <desc> - <p>Deletes the digraph <c><anno>G</anno></c>. This call is important - because digraphs are implemented with <c>ETS</c>. There is - no garbage collection of <c>ETS</c> tables. The digraph - will, however, be deleted if the process that created the - digraph terminates. - </p> + <p>Deletes digraph <c><anno>G</anno></c>. This call is important + as digraphs are implemented with ETS. There is + no garbage collection of ETS tables. However, the digraph + is deleted if the process that created the digraph terminates.</p> </desc> </func> + <func> <name name="edge" arity="2"/> - <fsummary>Return the vertices and the label of an edge of a digraph.</fsummary> + <fsummary>Return the vertices and the label of an edge of a digraph. + </fsummary> <desc> - <p>Returns <c>{<anno>E</anno>, <anno>V1</anno>, <anno>V2</anno>, <anno>Label</anno>}</c> where - <c><anno>Label</anno></c> is the <seealso marker="#label">label</seealso> - of the edge - <c><anno>E</anno></c> <seealso marker="#emanate">emanating</seealso> from - <c><anno>V1</anno></c> and <seealso marker="#incident">incident</seealso> on - <c><anno>V2</anno></c> of the digraph <c><anno>G</anno></c>. - If there is no edge <c><anno>E</anno></c> of the - digraph <c><anno>G</anno></c>, then <c>false</c> is returned. - </p> + <p>Returns + <c>{<anno>E</anno>, <anno>V1</anno>, <anno>V2</anno>, <anno>Label</anno>}</c>, + where <c><anno>Label</anno></c> is the + <seealso marker="#label">label</seealso> of edge + <c><anno>E</anno></c> <seealso marker="#emanate">emanating</seealso> + from <c><anno>V1</anno></c> and + <seealso marker="#incident">incident</seealso> on + <c><anno>V2</anno></c> of digraph <c><anno>G</anno></c>. + If no edge <c><anno>E</anno></c> of + digraph <c><anno>G</anno></c> exists, <c>false</c> is returned.</p> </desc> </func> + <func> <name name="edges" arity="1"/> <fsummary>Return all edges of a digraph.</fsummary> <desc> - <p>Returns a list of all edges of the digraph <c><anno>G</anno></c>, in - some unspecified order. - </p> + <p>Returns a list of all edges of digraph <c><anno>G</anno></c>, in + some unspecified order.</p> </desc> </func> + <func> <name name="edges" arity="2"/> - <fsummary>Return the edges emanating from or incident on a vertex of a digraph.</fsummary> + <fsummary>Return the edges emanating from or incident on a vertex of + a digraph.</fsummary> <desc> - <p>Returns a list of all - edges <seealso marker="#emanate">emanating</seealso> from - or <seealso marker="#incident">incident</seealso> on <c><anno>V</anno></c> - of the digraph <c><anno>G</anno></c>, in some unspecified order.</p> + <p>Returns a list of all + edges <seealso marker="#emanate">emanating</seealso> from or + <seealso marker="#incident">incident</seealso> on<c><anno>V</anno></c> + of digraph <c><anno>G</anno></c>, in some unspecified order.</p> </desc> </func> + <func> <name name="get_cycle" arity="2"/> <fsummary>Find one cycle in a digraph.</fsummary> <desc> - <p>If there is - a <seealso marker="#simple_cycle">simple cycle</seealso> of - length two or more through the vertex - <c><anno>V</anno></c>, then the cycle is returned as a list - <c>[<anno>V</anno>, ..., <anno>V</anno>]</c> of vertices, otherwise if there - is a <seealso marker="#loop">loop</seealso> through - <c><anno>V</anno></c>, then the loop is returned as a list <c>[<anno>V</anno>]</c>. If - there are no cycles through <c><anno>V</anno></c>, then <c>false</c> is - returned. - </p> - <p><c>get_path/3</c> is used for finding a simple cycle - through <c><anno>V</anno></c>. - </p> + <p>If a <seealso marker="#simple_cycle">simple cycle</seealso> of + length two or more exists through vertex <c><anno>V</anno></c>, the + cycle is returned as a list + <c>[<anno>V</anno>, ..., <anno>V</anno>]</c> of vertices. + If a <seealso marker="#loop">loop</seealso> through + <c><anno>V</anno></c> exists, the loop is returned as a list + <c>[<anno>V</anno>]</c>. If no cycles through + <c><anno>V</anno></c> exist, <c>false</c> is returned.</p> + <p><seealso marker="#get_path/3"><c>get_path/3</c></seealso> is used + for finding a simple cycle through <c><anno>V</anno></c>.</p> </desc> </func> + <func> <name name="get_path" arity="3"/> <fsummary>Find one path in a digraph.</fsummary> <desc> - <p>Tries to find - a <seealso marker="#simple_path">simple path</seealso> from - the vertex <c><anno>V1</anno></c> to the vertex - <c><anno>V2</anno></c> of the digraph <c><anno>G</anno></c>. Returns the path as a - list <c>[<anno>V1</anno>, ..., <anno>V2</anno>]</c> of vertices, or - <c>false</c> if no simple path from <c><anno>V1</anno></c> to <c><anno>V2</anno></c> - of length one or more exists. - </p> - <p>The digraph <c><anno>G</anno></c> is traversed in a depth-first manner, - and the first path found is returned. - </p> + <p>Tries to find + a <seealso marker="#simple_path">simple path</seealso> from vertex + <c><anno>V1</anno></c> to vertex <c><anno>V2</anno></c> of digraph + <c><anno>G</anno></c>. Returns the path as a list + <c>[<anno>V1</anno>, ..., <anno>V2</anno>]</c> of vertices, + or <c>false</c> if no simple path from <c><anno>V1</anno></c> to + <c><anno>V2</anno></c> of length one or more exists.</p> + <p>Digraph <c><anno>G</anno></c> is traversed in a depth-first manner, + and the first found path is returned.</p> </desc> </func> + <func> <name name="get_short_cycle" arity="2"/> <fsummary>Find one short cycle in a digraph.</fsummary> <desc> - <p>Tries to find an as short as - possible <seealso marker="#simple_cycle">simple cycle</seealso> through - the vertex <c><anno>V</anno></c> of the digraph <c>G</c>. Returns the cycle - as a list <c>[<anno>V</anno>, ..., <anno>V</anno>]</c> of vertices, or + <p>Tries to find an as short as possible + <seealso marker="#simple_cycle">simple cycle</seealso> through + vertex <c><anno>V</anno></c> of digraph <c>G</c>. Returns the cycle + as a list <c>[<anno>V</anno>, ..., <anno>V</anno>]</c> + of vertices, or <c>false</c> if no simple cycle through <c><anno>V</anno></c> exists. - Note that a <seealso marker="#loop">loop</seealso> through - <c><anno>V</anno></c> is returned as the list <c>[<anno>V</anno>, <anno>V</anno>]</c>. - </p> - <p><c>get_short_path/3</c> is used for finding a simple cycle - through <c><anno>V</anno></c>. - </p> + Notice that a <seealso marker="#loop">loop</seealso> through + <c><anno>V</anno></c> is returned as list + <c>[<anno>V</anno>, <anno>V</anno>]</c>.</p> + <p><seealso marker="#get_short_path/3"><c>get_short_path/3</c></seealso> + is used for finding a simple cycle through <c><anno>V</anno></c>.</p> </desc> </func> + <func> <name name="get_short_path" arity="3"/> <fsummary>Find one short path in a digraph.</fsummary> <desc> - <p>Tries to find an as short as - possible <seealso marker="#simple_path">simple path</seealso> from - the vertex <c><anno>V1</anno></c> to the vertex <c><anno>V2</anno></c> of the digraph <c><anno>G</anno></c>. - Returns the path as a list <c>[<anno>V1</anno>, ..., <anno>V2</anno>]</c> of - vertices, or <c>false</c> if no simple path from <c><anno>V1</anno></c> - to <c><anno>V2</anno></c> of length one or more exists. - </p> - <p>The digraph <c><anno>G</anno></c> is traversed in a breadth-first - manner, and the first path found is returned. - </p> + <p>Tries to find an as short as possible + <seealso marker="#simple_path">simple path</seealso> from vertex + <c><anno>V1</anno></c> to vertex <c><anno>V2</anno></c> of digraph + <c><anno>G</anno></c>. Returns the path as a list + <c>[<anno>V1</anno>, ..., <anno>V2</anno>]</c> of + vertices, or <c>false</c> if no simple path from + <c><anno>V1</anno></c> + to <c><anno>V2</anno></c> of length one or more exists.</p> + <p>Digraph <c><anno>G</anno></c> is traversed in a breadth-first + manner, and the first found path is returned.</p> </desc> </func> + <func> <name name="in_degree" arity="2"/> <fsummary>Return the in-degree of a vertex of a digraph.</fsummary> <desc> - <p>Returns the <seealso marker="#in_degree">in-degree</seealso> of the vertex - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>. - </p> + <p>Returns the <seealso marker="#in_degree">in-degree</seealso> of + vertex <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="in_edges" arity="2"/> - <fsummary>Return all edges incident on a vertex of a digraph.</fsummary> + <fsummary>Return all edges incident on a vertex of a digraph.</fsummary> <desc> - <p>Returns a list of all - edges <seealso marker="#incident">incident</seealso> on - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>, in some unspecified order. - </p> + <p>Returns a list of all + edges <seealso marker="#incident">incident</seealso> on + <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>, + in some unspecified order.</p> </desc> </func> + <func> <name name="in_neighbours" arity="2"/> - <fsummary>Return all in-neighbours of a vertex of a digraph.</fsummary> + <fsummary>Return all in-neighbors of a vertex of a digraph.</fsummary> <desc> - <p>Returns a list of - all <seealso marker="#in_neighbour">in-neighbours</seealso> of - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>, in some unspecified order. - </p> + <p>Returns a list of + all <seealso marker="#in_neighbour">in-neighbors</seealso> of + <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>, + in some unspecified order.</p> </desc> </func> + <func> <name name="info" arity="1"/> <fsummary>Return information about a digraph.</fsummary> <type name="d_cyclicity"/> <type name="d_protection"/> <desc> - <p>Returns a list of <c>{Tag, Value}</c> pairs describing the - digraph <c><anno>G</anno></c>. The following pairs are returned: - </p> + <p>Returns a list of <c>{Tag, Value}</c> pairs describing + digraph <c><anno>G</anno></c>. The following pairs are returned:</p> <list type="bulleted"> <item> - <p><c>{cyclicity, <anno>Cyclicity</anno>}</c>, where <c><anno>Cyclicity</anno></c> + <p><c>{cyclicity, <anno>Cyclicity</anno>}</c>, where + <c><anno>Cyclicity</anno></c> is <c>cyclic</c> or <c>acyclic</c>, according to the options given to <c>new</c>.</p> </item> <item> - <p><c>{memory, <anno>NoWords</anno>}</c>, where <c><anno>NoWords</anno></c> is - the number of words allocated to the <c>ETS</c> tables.</p> + <p><c>{memory, <anno>NoWords</anno>}</c>, where + <c><anno>NoWords</anno></c> is + the number of words allocated to the ETS tables.</p> </item> <item> - <p><c>{protection, <anno>Protection</anno>}</c>, where <c><anno>Protection</anno></c> + <p><c>{protection, <anno>Protection</anno>}</c>, where + <c><anno>Protection</anno></c> is <c>protected</c> or <c>private</c>, according to the options given to <c>new</c>.</p> </item> </list> </desc> </func> + <func> <name name="new" arity="0"/> - <fsummary>Return a protected empty digraph, where cycles are allowed.</fsummary> + <fsummary>Return a protected empty digraph, where cycles are allowed. + </fsummary> <desc> - <p>Equivalent to <c>new([])</c>. - </p> + <p>Equivalent to <c>new([])</c>.</p> </desc> </func> + <func> <name name="new" arity="1"/> <fsummary>Create a new empty digraph.</fsummary> @@ -415,97 +465,103 @@ <type name="d_cyclicity"/> <type name="d_protection"/> <desc> - <p>Returns - an <seealso marker="#empty_digraph">empty digraph</seealso> with - properties according to the options in <c><anno>Type</anno></c>:</p> + <p>Returns + an <seealso marker="#empty_digraph">empty digraph</seealso> with + properties according to the options in <c><anno>Type</anno></c>:</p> <taglist> <tag><c>cyclic</c></tag> - <item>Allow <seealso marker="#cycle">cycles</seealso> in the - digraph (default).</item> + <item><p>Allows <seealso marker="#cycle">cycles</seealso> in the + digraph (default).</p></item> <tag><c>acyclic</c></tag> - <item>The digraph is to be kept <seealso marker="#acyclic_digraph">acyclic</seealso>.</item> + <item><p>The digraph is to be kept + <seealso marker="#acyclic_digraph">acyclic</seealso>.</p></item> <tag><c>protected</c></tag> - <item>Other processes can read the digraph (default).</item> + <item><p>Other processes can read the digraph (default).</p></item> <tag><c>private</c></tag> - <item>The digraph can be read and modified by the creating - process only.</item> + <item><p>The digraph can be read and modified by the creating + process only.</p></item> </taglist> - <p>If an unrecognized type option <c>T</c> is given or <c><anno>Type</anno></c> - is not a proper list, there will be a <c>badarg</c> exception. - </p> + <p>If an unrecognized type option <c>T</c> is specified or + <c><anno>Type</anno></c> + is not a proper list, a <c>badarg</c> exception is raised.</p> </desc> </func> + <func> <name name="no_edges" arity="1"/> - <fsummary>Return the number of edges of the a digraph.</fsummary> + <fsummary>Return the number of edges of a digraph.</fsummary> <desc> - <p>Returns the number of edges of the digraph <c><anno>G</anno></c>. - </p> + <p>Returns the number of edges of digraph <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="no_vertices" arity="1"/> <fsummary>Return the number of vertices of a digraph.</fsummary> <desc> - <p>Returns the number of vertices of the digraph <c><anno>G</anno></c>. - </p> + <p>Returns the number of vertices of digraph <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="out_degree" arity="2"/> <fsummary>Return the out-degree of a vertex of a digraph.</fsummary> <desc> - <p>Returns the <seealso marker="#out_degree">out-degree</seealso> of the vertex - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>. - </p> + <p>Returns the <seealso marker="#out_degree">out-degree</seealso> of + vertex <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>.</p> </desc> </func> + <func> <name name="out_edges" arity="2"/> - <fsummary>Return all edges emanating from a vertex of a digraph.</fsummary> + <fsummary>Return all edges emanating from a vertex of a digraph. + </fsummary> <desc> - <p>Returns a list of all - edges <seealso marker="#emanate">emanating</seealso> from - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>, in some unspecified order. - </p> + <p>Returns a list of all + edges <seealso marker="#emanate">emanating</seealso> from + <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>, + in some unspecified order.</p> </desc> </func> + <func> <name name="out_neighbours" arity="2"/> - <fsummary>Return all out-neighbours of a vertex of a digraph.</fsummary> + <fsummary>Return all out-neighbors of a vertex of a digraph.</fsummary> <desc> <p>Returns a list of - all <seealso marker="#out_neighbour">out-neighbours</seealso> of - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>, in some unspecified order. - </p> + all <seealso marker="#out_neighbour">out-neighbors</seealso> of + <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>, + in some unspecified order.</p> </desc> </func> + <func> <name name="vertex" arity="2"/> <fsummary>Return the label of a vertex of a digraph.</fsummary> <desc> - <p>Returns <c>{<anno>V</anno>, <anno>Label</anno>}</c> where <c><anno>Label</anno></c> is the + <p>Returns <c>{<anno>V</anno>, <anno>Label</anno>}</c>, + where <c><anno>Label</anno></c> is the <seealso marker="#label">label</seealso> of the vertex - <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>, or <c>false</c> if there - is no vertex <c><anno>V</anno></c> of the digraph <c><anno>G</anno></c>. - </p> + <c><anno>V</anno></c> of digraph <c><anno>G</anno></c>, + or <c>false</c> if no vertex <c><anno>V</anno></c> + of digraph <c><anno>G</anno></c> exists.</p> </desc> </func> + <func> <name name="vertices" arity="1"/> <fsummary>Return all vertices of a digraph.</fsummary> <desc> - <p>Returns a list of all vertices of the digraph <c><anno>G</anno></c>, in - some unspecified order. - </p> + <p>Returns a list of all vertices of digraph <c><anno>G</anno></c>, in + some unspecified order.</p> </desc> </func> </funcs> <section> <title>See Also</title> - <p><seealso marker="digraph_utils">digraph_utils(3)</seealso>, - <seealso marker="ets">ets(3)</seealso></p> + <p><seealso marker="digraph_utils"><c>digraph_utils(3)</c></seealso>, + <seealso marker="ets"><c>ets(3)</c></seealso></p> </section> </erlref> |