Quelle z-appA.xml Sprache: XML

<Appendix>
  <Heading>
    Grape to Digraphs Command Map
  </Heading>
  Below is a table of &GRAPE; commands with the &Digraphs; counterparts.
  The sections in this chapter correspond to the chapters in the &GRAPE;
  manual.

  <Section>
    <Heading>
      Functions to construct and modify graphs
    </Heading>
    <Alt Not="HTML">
      <E>
        The table in this section contains more information when viewed in
        html format.
      </E>
    </Alt>

    <Table Align="|l|l|l|">
      <HorLine/>
      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Graph</C>
        </Item>
        <Item>
          <Ref Oper="Digraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
          Used with the arguments of <C>Graph</C> in &GRAPE;, <Ref
            Oper="Digraph"/> will return an equivalent digraph. <P/>
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>EdgeOrbitsGraph</C>
        </Item>
        <Item>
          <Ref Oper="EdgeOrbitsDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
          The operation <Ref Oper="EdgeOrbitsDigraph"/> behaves the same as
          <C>EdgeOrbitsDigraph</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>NullGraph</C>
        </Item>
        <Item>
          <Ref Oper="NullDigraph"/>
          <Alt Only="HTML">
            or
            <Ref Oper="EmptyDigraph"/>
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            Note that, unlike in &GRAPE;, the arguments of  <Ref
              Oper="NullDigraph"/> and <Ref Oper="EmptyDigraph"/> are just
            non-negative integers. Since digraphs in &Digraphs; are immutable,
            there is no reason (although it is possible) to create a null digraph
            and then add edges, as you might be used to doing in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CompleteGraph</C>
        </Item>
        <Item>
          <Ref Oper="CompleteDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            Note that, unlike in &GRAPE;, the argument to <Ref
              Oper="CompleteDigraph"/> is simply a non-negative integer
            indicating the number of vertices. By default a complete digraph in
            &Digraphs; does not have any loops. If you want a complete digraph
            with loops at every vertex, then use <Ref
              Oper="DigraphAddAllLoops"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>JohnsonGraph</C>
        </Item>
        <Item>
          <Ref Oper="JohnsonDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>JohnsonGraph</C> is equivalent to
            <Ref Oper="JohnsonDigraph"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CayleyGraph</C>
        </Item>
        <Item>
          <Ref Oper="CayleyDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Oper="CayleyDigraph"/> behaves the same as
            <C>CayleyGraph</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>AddEdgeOrbit</C>
        </Item>
        <Item>
          <Ref Oper="DigraphAddEdgeOrbit"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            Note that, unlike in &GRAPE;, digraphs in &Digraphs; are immutable,
            and this operation returns a new digraph, i.e. it does not modify the
            digraph given as an argument.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>RemoveEdgeOrbit</C>
        </Item>
        <Item>
          <Ref Oper="DigraphRemoveEdgeOrbit"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            Note that, unlike in &GRAPE;, digraphs in &Digraphs; are immutable,
            and this operation returns a new digraph, i.e. it does not modify the
            digraph given as an argument.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>AssignVertexNames</C>
        </Item>
        <Item>
          <Ref Oper="SetDigraphVertexLabels"/>
          <Alt Only="HTML">
            and
            <Ref Oper="SetDigraphVertexLabel"/>
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            Use  <Ref Oper="SetDigraphVertexLabel"/> to set an individual
            vertex label and <Ref Oper="SetDigraphVertexLabels"/> to set all of
            the vertex labels.
          </Alt>
        </Item>
      </Row>
      <HorLine/>
    </Table>
  </Section>

  <Section>
    <Heading>
      Functions to inspect graphs, vertices and edges
    </Heading>
    <Alt Not="HTML">
      <E>
        The table in this section contains more information when viewed in
        html format.
      </E>
    </Alt>

    <Table Align="|l|l|l|">
      <HorLine/>

      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsGraph</C>
        </Item>
        <Item>
          <Ref Filt="IsDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <Ref Filt="IsDigraph"/> is a category and not a function like
            <C>IsGraph</C>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>OrderGraph</C>
        </Item>
        <Item>
          <Ref Attr="DigraphNrVertices"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Attr="DigraphNrVertices"/> behaves the same as
            <C>OrderGraph</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsVertex(<A>graph</A>, <A>v</A>)</C>
        </Item>
        <Item>
          <C><A>v</A> in DigraphVertices(<A>digraph</A>)</C>
        </Item>
        <Item>
          <Alt Only="HTML">
            The attribute <Ref Attr="DigraphVertices"/> can be used to return
            the list of vertices of a digraph, or if <A>v</A> is known to be
            a positive integer, then you can simply do
            <C><A>v</A> <= DigraphNrVertices(<A>digraph</A>)</C>
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>VertexName</C>
        </Item>
        <Item>
          <Ref Oper="DigraphVertexLabel"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            Unlike <C>VertexName</C> in &GRAPE;, the return value of
            <Ref Oper="DigraphVertexLabel"/> is mutable.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>VertexNames</C>
        </Item>
        <Item>
          <Ref Oper="DigraphVertexLabels"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            Unlike <C>VertexNames</C> in &GRAPE;, the return value of
            <Ref Oper="DigraphVertexLabels"/> is mutable.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Vertices</C>
        </Item>
        <Item>
          <Ref Attr="DigraphVertices"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The vertices of a digraph in &Digraphs; is always the range <C>[1
              .. n]</C> where <C>n</C> is the number of vertices of the
            digraph.  The operation <Ref Attr="DigraphVertices"/> behaves the
            same as <C>Vertices</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>VertexDegree</C>
        </Item>
        <Item>
          <Ref Oper="OutDegreeOfVertex"/>
          <Alt Only="HTML">
            (see also: <Ref Oper="InDegreeOfVertex"/>)
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Oper="OutDegreeOfVertex"/> behaves the same as
            <C>VertexDegree</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>VertexDegrees</C>
        </Item>
        <Item>
          <Ref Attr="OutDegreeSet"/>
          <Alt Only="HTML">
            (see also:
            <Ref Attr="OutDegreeSequence"/>,
            <Ref Attr="OutDegrees"/>,
            <Ref Attr="InDegrees"/>,
            <Ref Attr="InDegreeSequence"/>,
            <Ref Attr="InDegreeSet"/>)
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Attr="OutDegreeSet"/> behaves the same as
            <C>VertexDegrees</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsLoopy</C>
        </Item>
        <Item>
          <Ref Prop="DigraphHasLoops"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Prop="DigraphHasLoops"/> behaves the same as
            <C>IsLoopy</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsSimpleGraph</C>
        </Item>
        <Item>
          <Alt Only="HTML">
            <Ref Prop="IsSymmetricDigraph"/>
            and not  <Ref Prop="DigraphHasLoops"/>
          </Alt>
          <Alt Not="HTML">
            <Ref Prop="IsSymmetricDigraph"/>
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>IsSimpleGraph</C> is equivalent to
            <Ref Prop="IsSymmetricDigraph"/>
            and not  <Ref Prop="DigraphHasLoops"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Adjacency</C>
        </Item>
        <Item>
          <Ref Oper="OutNeighboursOfVertex"/>
          <Alt Only="HTML">
            (see also <Ref Oper="InNeighboursOfVertex"/>)
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Oper="OutNeighboursOfVertex"/> behaves the same
            as <C>Adjacency</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsEdge</C>
        </Item>
        <Item>
          <Ref Oper="IsDigraphEdge" Label="for digraph and list"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The arguments of
            <Ref Oper="IsDigraphEdge" Label="for digraph and list"/>
            can be a digraph and an edge, or a digraph and two vertices. In the
            first form the operation
            <Ref Oper="IsDigraphEdge" Label="for digraph and list"/>
            behaves the same as <C>IsEdge</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>DirectedEdges</C>
        </Item>
        <Item>
          <Ref Attr="DigraphEdges"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The attribute <Ref Attr="DigraphEdges"/> behaves the same
            as <C>DirectedEdges</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>UndirectedEdges</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, and no plans to
            include one.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Distance</C>
        </Item>
        <Item>
          <Ref Oper="DigraphShortestDistance"
               Label="for a digraph and two vertices"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The operation <Ref Oper="DigraphShortestDistance"
            Label="for a digraph and two vertices"/> behaves the same as
            <C>Distance</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Diameter</C>
        </Item>
        <Item>
          <Ref Attr="DigraphDiameter"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The attribute <Ref Attr="DigraphDiameter"/> behaves the same
            as <C>Diameter</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Girth</C>
        </Item>
        <Item>
          <Ref Attr="DigraphUndirectedGirth"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The attribute <Ref Attr="DigraphUndirectedGirth"/> behaves the same
            as <C>Girth</C> in &GRAPE; except that in the case that the
            argument is a forest, <K>infinity</K> is returned by &Digraphs;
            whereas <C>-1</C> is returned by &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsConnectedGraph</C>
        </Item>
        <Item>
          <Ref Prop="IsStronglyConnectedDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The attribute <Ref Prop="IsStronglyConnectedDigraph"/> behaves the
            same as <C>IsConnectedGraph</C> in &GRAPE;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsBipartite</C>
        </Item>
        <Item>
          <Ref Prop="IsBipartiteDigraph"/>
          <Alt Only="HTML">
            and <Ref Prop="IsSymmetricDigraph"/>
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>IsBipartite</C> is equivalent to
            <Ref Prop="IsBipartiteDigraph"/> and <Ref
              Prop="IsSymmetricDigraph"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsNullGraph</C>
        </Item>
        <Item>
          <Ref Prop="IsNullDigraph"/>
          <Alt Only="HTML">
            or <Ref Prop="IsEmptyDigraph"/>
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>IsNullGraph</C> is equivalent to
            <Ref Prop="IsEmptyDigraph"/> and its synonym <Ref
              Prop="IsNullDigraph"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsCompleteGraph</C>
        </Item>
        <Item>
          <Ref Prop="IsCompleteDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>IsCompleteGraph</C> is roughly
            equivalent to
            <Ref Prop="IsCompleteDigraph"/> except that in &Digraphs;
            a complete digraph has <E>no loops</E>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

  </Table>
  </Section>

  <Section>
    <Heading>
      Functions to determine regularity properties of graphs
    </Heading>
    <Alt Not="HTML">
      <E>
        The table in this section contains more information when viewed in
        html format.
      </E>
    </Alt>

    <Table Align="|l|l|l|">
      <HorLine/>

      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsRegularGraph</C>
        </Item>
        <Item>
          <Ref Prop="IsOutRegularDigraph"/>
          <Alt Only="HTML">
            (see also
            <Ref Prop="IsInRegularDigraph"/>
            and
            <Ref Prop="IsRegularDigraph"/>)
          </Alt>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>IsRegularGraph</C> is
            equivalent to <Ref Prop="IsOutRegularDigraph"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>LocalParameters</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
         <Alt Only="HTML">
            The &GRAPE; function <C>LocalParameters</C> has no equivalent
            function in &Digraphs;, although this might change in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>GlobalParameters</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
         <Alt Only="HTML">
            The &GRAPE; function <C>GlobalParameters</C> has no equivalent
            function in &Digraphs;, although this might change in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsDistanceRegular</C>
        </Item>
        <Item>
          <Ref Prop="IsDistanceRegularDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The &GRAPE; function <C>IsDistanceRegular</C> is
            equivalent to <Ref Prop="IsDistanceRegularDigraph"/>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CollapsedAdjacencyMat</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
         <Alt Only="HTML">
            The &GRAPE; function <C>CollapsedAdjacencyMat</C> has no equivalent
            function in &Digraphs;, although this might change in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>OrbitalGraphColadjMats</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
         <Alt Only="HTML">
            The &GRAPE; function <C>OrbitalGraphColadjMats</C> has no equivalent
            function in &Digraphs;, although this might change in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>VertexTransitiveDRGs</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
         <Alt Only="HTML">
            The &GRAPE; function <C>VertexTransitiveDRGs</C> has no equivalent
            function in &Digraphs;, although this might change in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

    </Table>

  </Section>

  <Section>
    <Heading>
      Some special vertex subsets of a graph
    </Heading>
    <Alt Not="HTML">
      <E>
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        html format.
      </E>
    </Alt>

    <Table Align="|l|l|l|">
      <HorLine/>

      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>ConnectedComponent</C>
        </Item>
        <Item>
          <Ref Oper="DigraphConnectedComponent"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            When applied to a simple di/graph and a vertex,
            <C>ConnectedComponent</C> in &GRAPE; is equivalent to
            <Ref Oper="DigraphConnectedComponent"/>.
            <Ref Oper="DigraphConnectedComponent"/> can also be applied to
            non-simple graphs (in the language of &GRAPE;).
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>ConnectedComponents</C>
        </Item>
        <Item>
          <Ref Attr="DigraphConnectedComponents"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            When applied to a simple di/graph,
            <C>ConnectedComponents</C> in &GRAPE; is equivalent to
            <Ref Attr="DigraphConnectedComponents"/>.
            <Ref Attr="DigraphConnectedComponents"/> can also be applied to
            non-simple graphs (in the language of &GRAPE;).
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Bicomponents</C>
        </Item>
        <Item>
          <Ref Attr="DigraphBicomponents"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            When applied to a simple bipartite di/graph,
            <C>Bicomponents</C> in &GRAPE; is equivalent to
            <Ref Attr="DigraphBicomponents"/>.
            The definition of <Ref Prop="IsBipartiteDigraph"/> does not require
            its argument to be simple (in the language of &GRAPE;), i.e. the
            bipartite graphs in &GRAPE; are a proper subset of the bipartite
            digraphs in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>DistanceSet</C>
        </Item>
        <Item>
            <Ref Oper="DigraphDistanceSet"
              Label="for a digraph, a pos int, and an int"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>DistanceSet</C> in &GRAPE; is equivalent to
            <Ref Oper="DigraphDistanceSet"
              Label="for a digraph, a pos int, and an int"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>Layers</C>
        </Item>
        <Item>
          <Ref Oper="DigraphLayers"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>Layers</C> in &GRAPE; is equivalent to
            <Ref Oper="DigraphLayers"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IndependentSet</C>
        </Item>
        <Item>
          <Ref Func="DigraphIndependentSet"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>IndependentSet</C> in &GRAPE; is equivalent to
            <Ref Func="DigraphIndependentSet"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

    </Table>

  </Section>

  <Section>
    <Heading>
      Functions to construct new graphs from old
    </Heading>
    <Alt Not="HTML">
      <E>
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        html format.
      </E>
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    <Table Align="|l|l|l|">
      <HorLine/>

      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>InducedSubgraph</C>
        </Item>
        <Item>
          <Ref Oper="InducedSubdigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <Ref Oper="InducedSubdigraph"/> in &Digraphs; does not allow a third
            argument <C>G</C> specifying a group of automorphisms on the
            resultant graph. This may be included in a future release.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>DistanceSetInduced</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, and no plans to
            include one.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>DistanceGraph</C>
        </Item>
        <Item>
          <Ref Oper="DistanceDigraph" Label="for digraph and list"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>DistanceGraph</C> in &GRAPE; is equivalent to
            <Ref Oper="DistanceDigraph" Label="for digraph and list"/> in
            &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>ComplementGraph</C>
        </Item>
        <Item>
          <Ref Oper="DigraphDual"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <Ref Oper="DigraphDual"/> in &Digraphs; is equivalent to
            <C>ComplementGraph</C> in &GRAPE; with the optional argument
            <A>comploops</A> set to <K>true</K> (loops/nonloops are
            complemented).
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>PointGraph</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, and no plans to
            include one.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>EdgeGraph</C>
        </Item>
        <Item>
          <Ref Oper="EdgeUndirectedDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>EdgeGraph</C> in &GRAPE; is equivalent to
            <Ref Oper="EdgeUndirectedDigraph"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>SwitchedGraph</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, and no plans to
            include one.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>UnderlyingGraph</C>
        </Item>
        <Item>
          <Ref Oper="DigraphSymmetricClosure"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>UnderlyingGraph</C> in &GRAPE; is equivalent to
            <Ref Oper="DigraphSymmetricClosure"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>QuotientGraph</C>
        </Item>
        <Item>
          <Ref Oper="QuotientDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <Ref Oper="QuotientDigraph"/> in &Digraphs; takes a partition
            <C>p</C> of the vertices of the digraph, rather than a set of
            generating pairs.  Hence, the equivalence might not be
            group-invariant.  Also note that in &Digraphs; multiple edges may be
            created, whereas in &GRAPE; they are effectively combined into a
            single edge.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>BipartiteDouble</C>
        </Item>
        <Item>
          <Ref Oper="BipartiteDoubleDigraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>BipartiteDouble</C> in &GRAPE; is equivalent to
            <Ref Oper="BipartiteDoubleDigraph"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>GeodesicsGraph</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, and no plans to
            include one.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CollapsedIndependentOrbitsGraph</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, although this feature
            might be implemented in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CollapsedCompleteOrbitsGraph</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, although this feature
            might be implemented in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>NewGroupGraph</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;.  However, the same
            results would be possible by calling <Ref Oper="DigraphCopy"/> on
            the digraph to produce a copy <C>gr</C>, and then applying
            <C>SetDigraphGroup(gr, G)</C>.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

    </Table>

  </Section>

  <Section>
    <Heading>
      Vertex-Colouring and Complete Subgraphs
    </Heading>
    <Alt Not="HTML">
      <E>
        The table in this section contains more information when viewed in
        html format.
      </E>
    </Alt>

    <Table Align="|l|l|l|">
      <HorLine/>

      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>VertexColouring</C>
        </Item>
        <Item>
          <Ref Attr="DigraphGreedyColouring" Label="for a digraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>VertexColouring</C> in &GRAPE; is equivalent to <Ref
            Attr="DigraphGreedyColouring" Label="for a digraph"/> in &Digraphs;,
            except it returns a transformation rather than a list of vertex
            colors.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CompleteSubgraphs</C>
        </Item>
        <Item>
          <Ref Func="DigraphCliques"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            The functionality of <C>CompleteSubgraphs</C> in &GRAPE; is provided
            by <Ref Func="DigraphCliques"/> and <Ref Func="DigraphMaximalCliques"/>
            in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>CompleteSubgraphsOfGivenSize</C>
        </Item>
        <Item>
          <Ref Func="DigraphCliques"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            Much of the functionality of <C>CompleteSubgraphsOfGivenSize</C> in
            &GRAPE; is provided by <Ref Func="DigraphCliques"/> and <Ref
              Func="DigraphMaximalCliques"/> in &Digraphs;, except that the
            functionality relating to vertex weights and partial colourings is
            not implemented.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

    </Table>
  </Section>

  <Section>
    <Heading>
      Automorphism groups and isomorphism testing for graphs
    </Heading>
    <Alt Not="HTML">
      <E>
        The table in this section contains more information when viewed in
        html format.
      </E>
    </Alt>

    <Table Align="|l|l|l|">
      <HorLine/>

      <Row>
        <Item>
          &GRAPE; command
        </Item>
        <Item>
          &Digraphs; command
        </Item>
        <Item>
          <Alt Only="HTML">
            Comments
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>AutGroupGraph</C>
        </Item>
        <Item>
          <Ref Attr="AutomorphismGroup" Label="for a digraph"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>AutGroupGraph</C> in &GRAPE; is equivalent to
            <Ref Attr="AutomorphismGroup" Label="for a digraph"/> in &Digraphs;.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>GraphIsomorphism</C>
        </Item>
        <Item>
          <Ref Oper="IsomorphismDigraphs" Label="for digraphs"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>GraphIsomorphism</C> in &GRAPE; is equivalent to <Ref
            Oper="IsomorphismDigraphs" Label="for digraphs"/> in &Digraphs;.
            Note however that <C>GraphIsomorphism</C>'s optional argument
            <A>firstunbindcanon</A> is not applicable, since the canonical
            labellings of a digraph are not portable between sessions.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>IsIsomorphicGraph</C>
        </Item>
        <Item>
          <Ref Oper="IsIsomorphicDigraph" Label="for digraphs"/>
        </Item>
        <Item>
          <Alt Only="HTML">
            <C>IsIsomorphicGraph</C> in &GRAPE; is equivalent to <Ref
            Oper="IsIsomorphicDigraph" Label="for digraphs"/> in &Digraphs;.
            Note however that <C>IsIsomorphicGraph</C>'s optional argument
            <A>firstunbindcanon</A> is not applicable, since the canonical
            labellings of a digraph are not portable between sessions.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

      <Row>
        <Item>
          <C>GraphIsomorphismClassRepresentatives</C>
        </Item>
        <Item>
          None
        </Item>
        <Item>
          <Alt Only="HTML">
            There is no analogous function in &Digraphs;, although this feature
            might be implemented in the future.
          </Alt>
        </Item>
      </Row>
      <HorLine/>

    </Table>
  </Section>
</Appendix>

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