% tkz-graph.sty v2.20c
% Copyright 2007-2026  Alain Matthes
% SPDX-License-Identifier: LPPL-1.3c
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3c
% of this license or (at your option) any later version.
% The latest version of this license is in
%   http://www.latex-project.org/lppl.txt
% and version 1.3c or later is part of all distributions of LaTeX
% version 2005/12/01 or later.
%
% This work has the LPPL maintenance status “maintained”.
%
% The Current Maintainer of this work is Alain Matthes.

%<--------------------------------------------------------------------------->
% Objet :  Création de graphes
%<--------------------------------------------------------------------------->
% v2.2 (2026/10/19) -- internal code, no change for the existing documents
%  - short names (\Vertex, \Vertices, \Edge, \Edges, \Loop, \EA, \WE, \NO,
%    \SO, \NOEA, \NOWE, \SOEA, \SOWE) : the code uses only the internal
%    commands \tkzgr@<name> ; the short names are installed at the
%    beginning of each tikzpicture, so a definition of \EA (or \NO...)
%    by the user or by another package is no longer a problem :
%    outside the pictures it keeps its meaning, inside the pictures
%    \EA is the command of tkz-graph.
%  - new names always available : \tkzVertex, \tkzVertices, \tkzEdge,
%    \tkzEdges, \tkzLoop, \tkzEA, \tkzWE, \tkzNO, \tkzSO, \tkzNOEA,
%    \tkzNOWE, \tkzSOEA, \tkzSOWE
%  - option noshortnames : the short names are never defined
%  - vstyle : each style is a key /tkzgraph/vstyle/<name> ; a new style
%    can be added with \tkzDefGraphStyle{<name>}{<code>}
%  - internal macros protected (\tkzgr@...) ; ifthen is no longer used
%    internally (but still loaded) ; etex removed ; \fileversion and
%    \filedate are no longer redefined
% v2.1 (2026/10/07) -- keys, no change for the user
%  - keys : xkeyval replaced by pgfkeys (already loaded by TikZ) ;
%    same names, same default values, same results
%  - the behaviour of xkeyval is kept : the preset values (\presetkeys)
%    are applied only to the keys that are not given by the user, and
%    the macros \SetVertexMath, \SetUpEdge, \GraphInit ... still change
%    these preset values
%  - vstyle (\GraphInit) and dir (\grLoop) are still case insensitive
%  - the internal macros keep their names (\cmdGR@<family>@<key>,
%    \ifGR@<family>@<key>) ; tkz-berge 2.2 uses the same layer
%  - correction : a second \GraphInit[vstyle=...] in the same group was
%    ignored (and wrote its value in the text)
%  - xkeyval is no longer loaded : a document that used it without
%    loading it must now load it
%  - tkz-berge older than 2.2 needs xkeyval and the old tkz-graph
% v2.00 (2021/01/20) -- CTAN version
%<--------------------------------------------------------------------------->
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{tkz-graph}[2026/10/20 v2.20c base for graphs]
%<--------------------------------------------------------------------------->
\newif\iftkzgr@short
\tkzgr@shorttrue
\DeclareOption{noshortnames}{\tkzgr@shortfalse}
\ProcessOptions\relax
% ifthen is no longer used by tkz-graph ; it is still loaded for the
% documents (and tkz-berge) that use \ifthenelse without loading it
\RequirePackage{ifthen}
\RequirePackage{tikz}
\usetikzlibrary{arrows}
%<--------------------------------------------------------------------------->
%            Keys : a small layer on pgfkeys (replaces xkeyval)
%<--------------------------------------------------------------------------->
% All the keys live in /tkzgraph/<family>/<key>. The macros below
% reproduce the xkeyval commands used before 2.1 :
%  \tkzgr@cmdkey{fam}{key}          \define@cmdkey[GR]{fam}{key}{}
%  \tkzgr@cmdkeydef{fam}{key}{def}  \define@cmdkey[GR]{fam}{key}[def]{}
%  \tkzgr@boolkey{fam}{key}         \define@boolkey[GR]{fam}{key}[true]{}
%  \tkzgr@choicekey{fam}{key}{list}{code}
%                                   \define@choicekey*[GR]{fam}{key}[\val\nr]
%                                                     {list}{code}
%  \tkzgr@presetkeys{fam}{k=v,...}  \presetkeys[GR]{fam}{k=v,...}{}
%  \tkzgr@setkeys{fam}{k=v,...}     \setkeys[GR]{fam}{k=v,...}
% A key "key" of the family "fam" stores its value in \cmdGR@fam@key
% (or sets the boolean \ifGR@fam@key), as xkeyval did.
%<--------------------------------------------------------------------------->
\def\tkzgr@cmdkey#1#2{%
  \expandafter\tkzgr@cmdkey@\csname cmdGR@#1@#2\endcsname{#1}{#2}}
\def\tkzgr@cmdkey@#1#2#3{\pgfkeys{/tkzgraph/#2/#3/.store in=#1}}
\def\tkzgr@cmdkeydef#1#2#3{%
  \tkzgr@cmdkey{#1}{#2}%
  \pgfkeys{/tkzgraph/#1/#2/.default={#3}}}
\def\tkzgr@boolkey#1#2{%
  \expandafter\newif\csname ifGR@#1@#2\endcsname
  \pgfkeys{/tkzgraph/#1/#2/.is if  = GR@#1@#2,
           /tkzgraph/#1/#2/.default = true}}
%<--------------------------------------------------------------------------->
% choice keys : the value is compared without case ; \val is the value
% found in the list, \nr its rank (0,1,...) ; then <code> is executed
\def\tkzgr@choicekey#1#2#3#4{%
  \expandafter\def\csname tkzgr@cl@#1@#2\endcsname{#3}%
  \expandafter\def\csname tkzgr@cc@#1@#2\endcsname{#4}%
  \pgfkeys{/tkzgraph/#1/#2/.code={\tkzgr@dochoice{#1}{#2}{##1}}}}
\def\tkzgr@dochoice#1#2#3{%
  \edef\tkzgr@cv{#3}%
  \tkzgr@lowercase\tkzgr@cv
  \def\nr{-1}%
  \@tempcnta\z@
  \expandafter\expandafter\expandafter\@for
  \expandafter\expandafter\expandafter\tkzgr@c
  \expandafter\expandafter\expandafter:%
  \expandafter\expandafter\expandafter=%
  \csname tkzgr@cl@#1@#2\endcsname\do{%
    \let\tkzgr@lc\tkzgr@c
    \tkzgr@lowercase\tkzgr@lc
    \ifx\tkzgr@lc\tkzgr@cv
      \edef\nr{\the\@tempcnta}%
      \let\val\tkzgr@c
    \fi
    \advance\@tempcnta\@ne}%
  \ifnum\nr<\z@
    \PackageError{tkz-graph}{Value `#3' is not allowed for the key `#2'}%
      {Allowed values: \csname tkzgr@cl@#1@#2\endcsname}%
  \else
    \csname tkzgr@cc@#1@#2\endcsname
  \fi}
\def\tkzgr@lowercase#1{%
  \lowercase\expandafter{\expandafter\def\expandafter#1\expandafter{#1}}}
%<--------------------------------------------------------------------------->
% preset values : list of the names in \tkzgr@pl@<fam> (order of the
% first preset) and value of each key in \tkzgr@pv@<fam>@<key>.
% As with \presetkeys : a new value replaces the old one, local
% definitions (a group limits the change).
\def\tkzgr@novalue{\pgfkeysnovalue}
\pgfkeys{/tkzgraph/@preset/.unknown/.code = {\tkzgr@addpreset{#1}}}
\def\tkzgr@presetkeys#1#2{%
  \def\tkzgr@pfam{#1}%
  \pgfqkeys{/tkzgraph/@preset}{#2}}
\def\tkzgr@addpreset#1{%
  \edef\tkzgr@k{\pgfkeyscurrentname}%
  \expandafter\ifx\csname tkzgr@pl@\tkzgr@pfam\endcsname\relax
    \expandafter\let\csname tkzgr@pl@\tkzgr@pfam\endcsname\@empty
  \fi
  \edef\tkzgr@tmp{\noexpand\in@{,\tkzgr@k,}%
                  {,\csname tkzgr@pl@\tkzgr@pfam\endcsname,}}%
  \tkzgr@tmp
  \ifin@\else
    \expandafter\edef\csname tkzgr@pl@\tkzgr@pfam\endcsname{%
      \csname tkzgr@pl@\tkzgr@pfam\endcsname,\tkzgr@k}%
  \fi
  \expandafter\def\csname tkzgr@pv@\tkzgr@pfam @\tkzgr@k\endcsname{#1}}
%<--------------------------------------------------------------------------->
% \tkzgr@setkeys{fam}{list} : 1) the preset values of the keys absent
% from list, 2) list.
\pgfkeys{/tkzgraph/@mark/.unknown/.code = {%
  \edef\tkzgr@given{\tkzgr@given\pgfkeyscurrentname,}}}
\def\tkzgr@setkeys#1#2{%
  \def\tkzgr@given{,}%
  \pgfqkeys{/tkzgraph/@mark}{#2}%
  \let\tkzgr@todo\@empty
  \expandafter\let\expandafter\tkzgr@list\csname tkzgr@pl@#1\endcsname
  \ifx\tkzgr@list\relax\let\tkzgr@list\@empty\fi
  \@for\tkzgr@k:=\tkzgr@list\do{%
    \ifx\tkzgr@k\@empty\else
      \edef\tkzgr@tmp{\noexpand\in@{,\tkzgr@k,}{\tkzgr@given}}%
      \tkzgr@tmp
      \ifin@\else
        \expandafter\let\expandafter\tkzgr@v
          \csname tkzgr@pv@#1@\tkzgr@k\endcsname
        \ifx\tkzgr@v\tkzgr@novalue
          \edef\tkzgr@todo{\unexpanded\expandafter{\tkzgr@todo}\tkzgr@k,}%
        \else
          \edef\tkzgr@todo{\unexpanded\expandafter{\tkzgr@todo}%
            \tkzgr@k={\unexpanded\expandafter{\tkzgr@v}},}%
        \fi
      \fi
    \fi}%
  \edef\tkzgr@tmp{\noexpand\pgfqkeys{/tkzgraph/#1}%
                  {\unexpanded\expandafter{\tkzgr@todo}}}%
  \tkzgr@tmp
  \pgfqkeys{/tkzgraph/#1}{#2}}
% \tkzgr@ifempty{<text>}{<if empty>}{<if not empty>}
% (replaces \ifthenelse{\equal{<text>}{}}, same expansion)
\def\tkzgr@ifempty#1{%
  \protected@edef\tkzgr@tmpe{#1}%
  \ifx\tkzgr@tmpe\@empty
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi}
%<--------------------------------------------------------------------------->
% counters used by tkz-berge
\newcounter{tkz@gr@a}
\newcounter{tkz@gr@b}
\newcounter{tkz@gr@c}
\newcounter{tkz@gr@e}
\newcounter{tkz@gr@d}
\newcounter{tkz@gr@p}
\newcounter{tkz@gr@i}
\newcounter{tkz@gr@n}
\newcounter{tkz@gr@ta}
\newcounter{tkz@gr@tb}
%<--------------------------------------------------------------------------->
%                           Init vertex
%<--------------------------------------------------------------------------->
\def\tkz@gr@background@color{white}
\def\tkz@gr@text@color{black}
\global\edef\tkz@suc@bkc{\tkz@gr@background@color}
\global\edef\tkz@suc@txt{\tkz@gr@text@color}
\pgfkeys{
/tkzsupcol/.cd,
  background/.code    = {\global\edef\tkz@suc@bkc{#1}},
  text/.code          = {\global\edef\tkz@suc@txt{#1}},
}
\def\tkzSetUpColors{\pgfutil@ifnextchar[{\tkz@SetUpColors}{\tkz@SetUpColors[]}}
\def\tkz@SetUpColors[#1]{%
\begingroup
\pgfkeys{%
/tkzsupcol/.cd,
  background  = \tkz@gr@background@color,
  text        = \tkz@gr@text@color
  }
\pgfqkeys{/tkzsupcol}{#1}
\pagecolor{\tkz@suc@bkc}
\color{\tkz@suc@txt}
\endgroup
}

\newcommand*{\GraphUnit}{1}
\newcommand*{\VertexInnerSep}{2pt}
\newcommand*{\VertexOuterSep}{0pt}
\newcommand*{\VertexDistance}{3cm}
\newcommand*{\VertexShape}{circle}
\newcommand*{\VertexLineWidth}{0.5pt}
\newcommand*{\VertexLineColor}{\tkz@suc@txt}
\newcommand*{\VertexLightFillColor}{\tkz@suc@bkc}
\newcommand*{\VertexDarkFillColor}{\tkz@suc@txt}
\newcommand*{\VertexTextColor}{\tkz@suc@txt}
\newcommand*{\VertexFillColor}{\tkz@suc@txt}
\newcommand*{\VertexBallColor}{orange}
\newcommand*{\VertexBigMinSize}{24pt}
\newcommand*{\VertexInterMinSize}{18pt}
\newcommand*{\VertexSmallMinSize}{12pt}
\newcommand*{\EdgeFillColor}{orange}
\newcommand*{\EdgeArtColor}{orange}
\newcommand*{\EdgeColor}{\tkz@suc@txt}
\newcommand*{\EdgeDoubleDistance}{1pt}
\newcommand*{\EdgeLineWidth}{0.8pt}
\newcommand*{\LabelTextColor}{\tkz@suc@txt}
\newcommand*{\LabelFillColor}{\tkz@suc@bkc}

\tikzset{pre/.style={<-,shorten <=1pt,>=stealth',semithick}}
\tikzset{post/.style={->,shorten <=1pt,>=stealth',semithick}}
%<--------------------------------------------------------------------------->
%   Simple Vertex
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{SVS}{Shape}
\tkzgr@cmdkey{SVS}{MinSize}
\tkzgr@cmdkey{SVS}{LineWidth}
\tkzgr@cmdkey{SVS}{LineColor}
\tkzgr@cmdkey{SVS}{FillColor}
\tkzgr@cmdkey{SVS}{InnerSep}
\tkzgr@cmdkey{SVS}{OuterSep}
\tkzgr@presetkeys{SVS}{Shape          = \VertexShape,
                       MinSize        = \VertexSmallMinSize,
                       LineWidth      = \VertexLineWidth,
                       LineColor      = \VertexLineColor,
                       InnerSep       = \VertexInnerSep,
                       OuterSep       = \VertexOuterSep,
                       FillColor      = \VertexFillColor}
\newcommand*{\SetVertexSimple}[1][]{\tkzgr@SetVertexSimple[#1]}%
\def\tkzgr@SetVertexSimple[#1]{%
\tkzgr@setkeys{SVS}{#1}%
\tkzgr@presetkeys{vertex}{NoLabel           = true}%
\tikzset{VertexStyle/.style = {draw,
                               shape          = \cmdGR@SVS@Shape,
                               color          = \cmdGR@SVS@LineColor,
                               fill           = \cmdGR@SVS@FillColor,
                               inner sep      = \cmdGR@SVS@InnerSep,
                               outer sep      = \cmdGR@SVS@OuterSep,
                               minimum size   = \cmdGR@SVS@MinSize,
                               line width     = \cmdGR@SVS@LineWidth}}
\tikzset{EdgeStyle/.style   = {line width     = \EdgeLineWidth,
                                                \EdgeColor}}
\tikzset{LabelStyle/.style={}}}
%<--------------------------------------------------------------------------->
%   Shade Vertex
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{shade}{Shape}
\tkzgr@cmdkey{shade}{MinSize}
\tkzgr@cmdkey{shade}{LineWidth}
\tkzgr@cmdkey{shade}{LineColor}
\tkzgr@cmdkey{shade}{BallColor}
\tkzgr@cmdkey{shade}{InnerSep}
\tkzgr@cmdkey{shade}{OuterSep}
\tkzgr@presetkeys{shade}{Shape          = \VertexShape,
                         MinSize        = \VertexBigMinSize,
                         LineWidth      = \VertexLineWidth,
                         LineColor      = \VertexLineColor,
                         InnerSep       = \VertexInnerSep,
                         OuterSep       = \VertexOuterSep,
                         BallColor      = \VertexBallColor}
\newcommand*{\SetVertexShade}[1][]{\tkzgr@SetVertexShade[#1]}%
\def\tkzgr@SetVertexShade[#1]{%
\tkzgr@setkeys{shade}{#1}%
\tkzgr@presetkeys{vertex}{NoLabel           = false}%
\tikzset{VertexStyle/.style = {draw,
                               shape          = \cmdGR@shade@Shape,
                               ball color     = \cmdGR@shade@BallColor,
                               inner sep      = \cmdGR@shade@InnerSep,
                               outer sep      = \cmdGR@shade@OuterSep,
                               minimum size   = \cmdGR@shade@MinSize,
                               line width     = \VertexLineWidth}}
\tikzset{EdgeStyle/.style   = {line width     = \EdgeLineWidth,
                                                \EdgeColor,% color outside
                               double          = \EdgeFillColor,% inside
                               double distance = \EdgeDoubleDistance}}%
\tikzset{LabelStyle/.style={}}}
%<--------------------------------------------------------------------------->
%   Art Vertex
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{art}{Shape}
\tkzgr@cmdkey{art}{MinSize}
\tkzgr@cmdkey{art}{LineWidth}
\tkzgr@cmdkey{art}{LineColor}
\tkzgr@cmdkey{art}{BallColor}
\tkzgr@cmdkey{art}{InnerSep}
\tkzgr@cmdkey{art}{OuterSep}
\tkzgr@presetkeys{art}{Shape          = \VertexShape,
                       MinSize        = \VertexSmallMinSize,
                       LineWidth      = \VertexLineWidth,
                       LineColor      = \VertexLineColor,
                       InnerSep       = \VertexInnerSep,
                       OuterSep       = \VertexOuterSep,
                       BallColor      = \VertexBallColor}
\newcommand*{\SetVertexArt}[1][]{\tkzgr@SetVertexArt[#1]}%
\def\tkzgr@SetVertexArt[#1]{%
\tkzgr@setkeys{art}{#1}%
\tkzgr@presetkeys{vertex}{NoLabel               = true}%
\tikzset{VertexStyle/.style = {draw,
                               shape          = \cmdGR@art@Shape,
                               ball color     = \cmdGR@art@BallColor,
                               inner sep      = \cmdGR@art@InnerSep,
                               outer sep      = \cmdGR@art@OuterSep,
                               minimum size   = \cmdGR@art@MinSize,
                               line width     = \VertexLineWidth}}
\tikzset{EdgeStyle/.style   = {line width     = \EdgeLineWidth,
                                                 \EdgeArtColor}}
\tikzset{LabelStyle/.style  = {}}}
%<--------------------------------------------------------------------------->
%   Normal Vertex
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{SVN}{Shape}
\tkzgr@cmdkey{SVN}{MinSize}
\tkzgr@cmdkey{SVN}{LineWidth}
\tkzgr@cmdkey{SVN}{LineColor}
\tkzgr@cmdkey{SVN}{FillColor}
\tkzgr@cmdkey{SVN}{TextColor}
\tkzgr@cmdkey{SVN}{InnerSep}
\tkzgr@cmdkey{SVN}{OuterSep}
\tkzgr@presetkeys{SVN}{Shape              = \VertexShape,
                       MinSize            = \VertexInterMinSize,
                       LineWidth          = \VertexLineWidth,
                       LineColor          = \VertexLineColor,
                       FillColor          = \VertexLightFillColor,
                       InnerSep           = \VertexInnerSep,
                       OuterSep           = \VertexOuterSep,
                       TextColor          = \VertexTextColor}
\newcommand*{\SetVertexNormal}[1][]{\tkzgr@SetVertexNormal[#1]}%
\def\tkzgr@SetVertexNormal[#1]{%
\tkzgr@setkeys{SVN}{#1}%
\tikzset{VertexStyle/.style = {shape          = \cmdGR@SVN@Shape,
                               minimum size   = \cmdGR@SVN@MinSize,
                               line width     = \cmdGR@SVN@LineWidth,
                               color          = \cmdGR@SVN@LineColor,
                               fill           = \cmdGR@SVN@FillColor,
                               text           = \cmdGR@SVN@TextColor,
                               inner sep      = \cmdGR@SVN@InnerSep,
                               outer sep      = \cmdGR@SVN@OuterSep,
                               draw}}
\tikzset{EdgeStyle/.style   = {line width     = \EdgeLineWidth,
                                                 \EdgeColor}}
\tikzset{LabelStyle/.style={}}}
\SetVertexNormal% default
%<--------------------------------------------------------------------------->
%                    Graph styles (key vstyle of \GraphInit)
%<--------------------------------------------------------------------------->
% Each style is the key /tkzgraph/vstyle/<name> (name in lower case).
% \tkzDefGraphStyle{<name>}{<code>} defines (or redefines) a style ;
% \GraphInit[vstyle=<name>] executes <code> ; the name is case
% insensitive. Example :
%  \tkzDefGraphStyle{Red}{\GraphInit[vstyle=Normal]\SetGraphColor{red!20}{red}}
\newcommand{\tkzDefGraphStyle}[2]{%
  \edef\tkzgr@cv{#1}%
  \tkzgr@lowercase\tkzgr@cv
  \pgfkeys{/tkzgraph/vstyle/\tkzgr@cv/.code={#2}}}
\def\tkzgr@vstyle#1{%
  \edef\tkzgr@cv{#1}%
  \tkzgr@lowercase\tkzgr@cv
  \pgfkeysifdefined{/tkzgraph/vstyle/\tkzgr@cv/.@cmd}%
    {\pgfkeys{/tkzgraph/vstyle/\tkzgr@cv}}%
    {\PackageError{tkz-graph}{Value `#1' is not allowed for the key
       `vstyle'}{The styles are Empty, Hasse, Simple, Classic,
       Normal, Shade, Dijkstra, Welsh, Art, Shade Art and the styles
       defined with \string\tkzDefGraphStyle.}}}
% the styles Empty, Hasse, Simple, Classic, Dijkstra and Welsh differ
% only by these values :
% #1 preset of the key vertex (label), #2 draw or nothing,
% #3 fill, #4 outer sep, #5 minimum size
\def\tkzgr@basicvstyle#1#2#3#4#5{%
\tkzgr@presetkeys{vertex}{#1}%
\tikzset{VertexStyle/.style = {#2shape     = \VertexShape,
                               color          = \VertexLineColor,
                               fill           = #3,
                               inner sep      = \VertexInnerSep,
                               outer sep      = #4,
                               text           = \VertexTextColor,
                               minimum size   = #5,
                               line width     = \VertexLineWidth}}
\tikzset{EdgeStyle/.style   = {line width     = \EdgeLineWidth,
                                                \EdgeColor}}
\tikzset{LabelStyle/.style={}}}
\tkzDefGraphStyle{Empty}{%
  \tkzgr@basicvstyle{LabelOut = false}{}{\VertexLightFillColor}%
                    {0.5\pgflinewidth}{\VertexSmallMinSize}}
\tkzDefGraphStyle{Hasse}{%
  \tkzgr@basicvstyle{NoLabel = true}{draw,}{\VertexLightFillColor}%
                    {0.5\pgflinewidth}{\VertexSmallMinSize}}
\tkzDefGraphStyle{Simple}{%
  \tkzgr@basicvstyle{NoLabel = true}{draw,}{\VertexDarkFillColor}%
                    {0.5\pgflinewidth}{\VertexSmallMinSize}}
\tkzDefGraphStyle{Classic}{%
  \tkzgr@basicvstyle{LabelOut = true}{draw,}{\VertexDarkFillColor}%
                    {0.5\pgflinewidth}{\VertexSmallMinSize}}
\tkzDefGraphStyle{Dijkstra}{%
  \tkzgr@basicvstyle{LabelOut = false}{draw,}{\VertexLightFillColor}%
                    {0.5\pgflinewidth}{\VertexInterMinSize}}
\tkzDefGraphStyle{Welsh}{%
  \tkzgr@basicvstyle{LabelOut = true}{draw,}{\VertexLightFillColor}%
                    {\VertexOuterSep}{\VertexSmallMinSize}}
\tkzDefGraphStyle{Normal}{%
\tkzgr@presetkeys{vertex}{LabelOut            = false}%
\tikzset{VertexStyle/.style = {draw,
                               shape           = \VertexShape,
                               minimum size    = \VertexInterMinSize,
                               line width      = \VertexLineWidth,
                               color           = \VertexLineColor,
                               outer sep       = 0.5\pgflinewidth,
                               fill            = \VertexLightFillColor,
                               text            = \VertexTextColor,
                               line width      = \VertexLineWidth}}
\tikzset{EdgeStyle/.style   = {line width      = \EdgeLineWidth,
                                                 \EdgeColor}}
\tikzset{LabelStyle/.style={}}}
\tkzDefGraphStyle{Shade}{%
\tkzgr@presetkeys{vertex}{LabelOut            = false}%
\tikzset{VertexStyle/.style = {draw,
                               shape           = \VertexShape,
                               ball color      = \VertexBallColor,
                               color           = \VertexLineColor,
                               text            = \VertexTextColor,
                               inner sep       = \VertexInnerSep,
                               outer sep       = \VertexOuterSep,
                               minimum size    = \VertexBigMinSize,
                               line width      = \VertexLineWidth}}
\tikzset{EdgeStyle/.style   = {line width      = \EdgeLineWidth,
                                                 \EdgeColor,% color outside
                               double          = \EdgeFillColor,% inside
                               double distance = \EdgeDoubleDistance}}%
\tikzset{LabelStyle/.style={}}}
\tkzDefGraphStyle{Art}{%
\tkzgr@presetkeys{vertex}{NoLabel            = true}%
\tikzset{VertexStyle/.style = {shape          = \VertexShape,
                               ball color     = \VertexBallColor,
                               color          = \VertexLineColor,
                               inner sep      = \VertexInnerSep,
                               outer sep      = \VertexOuterSep,
                               minimum size   = \VertexSmallMinSize,
                               line width     = \VertexLineWidth}}%
\tikzset{EdgeStyle/.style   = {line width      = \EdgeLineWidth,
                                                 \EdgeArtColor}}
\tikzset{LabelStyle/.style  = {}}}
\tkzDefGraphStyle{Shade Art}{%
\tkzgr@presetkeys{vertex}{NoLabel            = true}%
\tikzset{VertexStyle/.style = {shape          = \VertexShape,
                               ball color     = \VertexBallColor,
                               inner sep      = \VertexInnerSep,
                               outer sep      = \VertexOuterSep,
                               minimum size   = \VertexSmallMinSize,
                               line width     = \VertexLineWidth}}
\tikzset{EdgeStyle/.style   = {line width      = \EdgeLineWidth,
                                                 \EdgeColor,
                               double          = \EdgeFillColor,
                               double distance = .5\EdgeDoubleDistance}}
\tikzset{LabelStyle/.style  = {}}}
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{init}{unit}
\pgfkeys{/tkzgraph/init/vstyle/.code = {\tkzgr@vstyle{#1}}}
\tkzgr@presetkeys{init}{vstyle     = Normal,%
                        unit       = \GraphUnit}

\newcommand*{\SetGraphUnit}[1]{\renewcommand{\GraphUnit}{#1}}%

\newcommand*{\GraphInit}[1][]{\tkzgr@setkeys{init}{#1}%
\edef\GraphUnit{\cmdGR@init@unit}%
}%
%<--------------------------------------------------------------------------->
%                             Colors
%<--------------------------------------------------------------------------->
\newcommand*{\SetGraphShadeColor}[3]{%
  \tikzset{VertexStyle/.append style = {ball color=#1}}
  \tikzset{EdgeStyle/.append style   = {color=#2,double=#3}}
}
\newcommand*{\SetGraphArtColor}[2]{%
  \tikzset{VertexStyle/.append style = {ball color=#1}}
  \tikzset{EdgeStyle/.append style   = {color=#2}}
}
\newcommand*{\SetGraphColor}[2]{%
  \tikzset{VertexStyle/.append style = {fill=#1}}
  \tikzset{EdgeStyle/.append style   = {color=#2}}
}
\newcommand*{\AddVertexColor}[2]{%
\begingroup
  \tikzset{VertexStyle/.append style  = {fill=#1}}
  \foreach \tkzgr@colv in {#2}
    {\tkzgr@Vertex[Node,NoLabel]{\tkzgr@colv}}
\endgroup
}
%<--------------------------------------------------------------------------->
\newcommand*{\SetVertexNoLabel}{%
    \tkzgr@presetkeys{vertex}{NoLabel = true}%
}
% add  RV
\newcommand*{\SetVertexLabel}{%
   \tkzgr@presetkeys{vertex}{NoLabel = false}%
}
%<--------------------------------------------------------------------------->
\newcommand*{\SetVertexLabelOut}{%
    \tkzgr@presetkeys{vertex}{LabelOut = true}%
}
\newcommand*{\SetVertexLabelIn}{%
    \tkzgr@presetkeys{vertex}{LabelOut = false}%
}
\newcommand*{\SetVertexMath}{%
    \tkzgr@presetkeys{vertex}{Math = true}%
    \tkzgr@presetkeys{cl}{Math = true}%
}
\newcommand*{\SetVertexNoMath}{%
    \tkzgr@presetkeys{vertex}{Math = false}%
    \tkzgr@presetkeys{cl}{Math = false}%
}
%<--------------------------------------------------------------------------->
%                          Init    SetUpVertex
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{SUV}{Lpos}
\tkzgr@cmdkey{SUV}{Ldist}
\tkzgr@cmdkey{SUV}{Style}
\tkzgr@cmdkey{SUV}{MinSize}
\tkzgr@cmdkey{SUV}{LineWidth}
\tkzgr@cmdkey{SUV}{TextColor}
\tkzgr@cmdkey{SUV}{LineColor}
\tkzgr@cmdkey{SUV}{FillColor}
\tkzgr@cmdkey{SUV}{InnerSep}
\tkzgr@cmdkey{SUV}{OuterSep}
\tkzgr@cmdkey{SUV}{Unit}
\tkzgr@boolkey{SUV}{NoLabel}
\tkzgr@boolkey{SUV}{LabelOut}
\tkzgr@boolkey{SUV}{Math}
\tkzgr@presetkeys{SUV}{Ldist     = 0cm,
                       Lpos      = 0,
                       Style     = {},
                       LabelOut  = false,
                       NoLabel   = false,
                       Math      = false,
                       Unit      = \GraphUnit,
                       MinSize   = \VertexInterMinSize,
                       TextColor = \VertexTextColor,
                       LineColor = \VertexLineColor,
                       FillColor = \VertexLightFillColor,
                       LineWidth = \VertexLineWidth,
                       InnerSep  = \VertexInnerSep,
                       OuterSep  = \VertexOuterSep}
%<--------------------------------------------------------------------------->
%                             SetUpVertex
%<--------------------------------------------------------------------------->
\newcommand*{\SetUpVertex}[1][]{\tkzgr@SetUpVertex[#1]}%
\def\tkzgr@SetUpVertex[#1]{%
\tkzgr@setkeys{SUV}{#1}%
\tkzgr@presetkeys{vertex}{Lpos     = \cmdGR@SUV@Lpos,
                          Ldist    = \cmdGR@SUV@Ldist,
                          style    = \cmdGR@SUV@Style,
                          unit     = \cmdGR@SUV@Unit}%
\tikzset{VertexStyle/.append style = {inner sep      = \cmdGR@SUV@InnerSep,
                                      outer sep      = \cmdGR@SUV@OuterSep,
                                      minimum size   = \cmdGR@SUV@MinSize,
                                      text           = \cmdGR@SUV@TextColor,
                                      color          = \cmdGR@SUV@LineColor,
                                      fill           = \cmdGR@SUV@FillColor,
                                      line width     = \cmdGR@SUV@LineWidth}}
\ifGR@SUV@NoLabel%
    \tkzgr@presetkeys{vertex}{NoLabel  = true}%
\fi%
\ifGR@SUV@LabelOut%
    \tkzgr@presetkeys{vertex}{LabelOut = true}%
\fi%
\ifGR@SUV@Math%
    \tkzgr@presetkeys{vertex}{Math = true}%
\fi%
}
%<--------------------------------------------------------------------------->
%                           Init Vertex
%<--------------------------------------------------------------------------->
\tkzgr@boolkey{vertex}{empty}
\tkzgr@cmdkey{vertex}{unit}
\tkzgr@cmdkey{vertex}{x}
\tkzgr@cmdkey{vertex}{y}
\tkzgr@cmdkey{vertex}{a}
\tkzgr@cmdkey{vertex}{d}
\tkzgr@boolkey{vertex}{Node}
\tkzgr@cmdkey{vertex}{dir}
\tkzgr@cmdkey{vertex}{style}
\tkzgr@cmdkey{vertex}{position}
\tkzgr@cmdkey{vertex}{L}
\tkzgr@cmdkey{vertex}{Lpos}
\tkzgr@cmdkey{vertex}{Ldist}
\tkzgr@boolkey{vertex}{NoLabel}
\tkzgr@boolkey{vertex}{Math}
\tkzgr@boolkey{vertex}{LabelOut}
\tkzgr@cmdkey{vertex}{rotation}
\tkzgr@boolkey{vertex}{clockwise}
\tkzgr@presetkeys{vertex}{Node      = false,
                          NoLabel   = false,
                          LabelOut  = false,
                          empty     = false,
                          Math      = false,
                          x         = {},
                          y         = {},
                          a         = {},
                          d         = {},
                          unit      = \GraphUnit,
                          dir       = \tkzgr@EA,
                          position  = {},
                          style     = {},
                          L         = {},
                          Ldist     = 0cm,
                          Lpos      = 0,
                          rotation  = 0,
                          clockwise = false}
%<--------------------------------------------------------------------------->
%                                  Vertex
%<--------------------------------------------------------------------------->
\newcommand*{\tkzgr@Vertex}[1][]{\tkzgr@vertex[#1]}%
\def\tkzgr@vertex[#1]#2{%
    \tkzgr@setkeys{vertex}{#1}%
    \tkzgr@@vertex{#2}%
}
% #1 name of the vertex
\def\tkzgr@@vertex#1{%
\tkzgr@recordvertex{#1}%
\def\tkzgr@nstyle{VertexStyle}%
%<--------------------------------------------------------------------------->
\ifGR@vertex@Node%
   \pgfextractx{\pgf@x}{\pgfpointanchor{#1}{center}}
   \pgfextracty{\pgf@y}{\pgfpointanchor{#1}{center}}
   \edef\cmdGR@vertex@x{\pgf@x}
   \edef\cmdGR@vertex@y{\pgf@y}
\fi%
%<--------------------------------------------------------------------------->
\ifGR@vertex@empty%
   \begin{scope}
      \tkzgr@ifempty{\cmdGR@vertex@x}{%
       \tkzgr@ifempty{\cmdGR@vertex@d}{%
           \protected@edef\@tempa{%
               \noexpand \node[inner sep = 0pt](#1)%
                  [\cmdGR@vertex@position]{}}%
           \@tempa;}{%
           \protected@edef\@tempa{%
               \noexpand\node[inner sep = 0pt](#1)%
                  at (\cmdGR@vertex@a:\cmdGR@vertex@d){}}%
           \@tempa;}}{%
           \protected@edef\@tempa{%
               \noexpand\node[inner sep = 0pt](#1)%
                  at (\cmdGR@vertex@x,\cmdGR@vertex@y){}}%
           \@tempa;}%
    \end{scope}
\else
 \begin{scope}[label distance = \cmdGR@vertex@Ldist]
  \ifGR@vertex@NoLabel
       \def\tkzgr@vertex@Label{}%
       \def\cmdGR@vertex@L{}%
       \def\tkzgr@vertex@Name{}%
  \else%
     \ifGR@vertex@Math
       \tkzgr@ifempty{\cmdGR@vertex@L}%
         {\def\tkzgr@vertex@Name{$#1$}}%
         {\def\tkzgr@vertex@Name{$\cmdGR@vertex@L$}}%
     \else
       \tkzgr@ifempty{\cmdGR@vertex@L}%
         {\def\tkzgr@vertex@Name{#1}}%
         {\def\tkzgr@vertex@Name{\cmdGR@vertex@L}}%
     \fi%
      \ifGR@vertex@LabelOut%
        \def\tkzgr@nstyle{VertexStyle,%
                    label={[text = \cmdGR@SVN@TextColor,\cmdGR@vertex@style]%
                    \cmdGR@vertex@Lpos:\tkzgr@vertex@Name}}%
        \def\tkzgr@vertex@Label{}%
      \else%
      \def\tkzgr@vertex@Label{\tkzgr@vertex@Name}%
      \fi
  \fi
%<--------------------------------------------------------------------------->
  \tkzgr@ifempty{\cmdGR@vertex@x}{%
      \tkzgr@ifempty{\cmdGR@vertex@d}{%
        \protected@edef\@tempa{%
        \noexpand\node[outer sep=0pt,\cmdGR@vertex@style,\tkzgr@nstyle](#1)%
                      [\cmdGR@vertex@position]{%
        \noexpand\tkzgr@vertex@Label}}%
       \@tempa;}{%
        \protected@edef\@tempa{%
        \noexpand\node[outer sep=0pt,\cmdGR@vertex@style,\tkzgr@nstyle](#1)
                       at (\cmdGR@vertex@a:\cmdGR@vertex@d){%
        \noexpand\tkzgr@vertex@Label}}%
        \@tempa;}}{%
    \protected@edef\@tempa{%
      \noexpand\node[outer sep=0pt,\cmdGR@vertex@style,\tkzgr@nstyle](#1)
                 at (\cmdGR@vertex@x,\cmdGR@vertex@y){%
      \noexpand\tkzgr@vertex@Label}}%
      \@tempa;}%
  \end{scope}
\fi%
}
%<--------------------------------------------------------------------------->
%                          End of  Vertex
%<--------------------------------------------------------------------------->
%    Relative position : \EA (east) \WE (west) \NO (north) \SO (south)
%                        \NOEA \NOWE \SOEA \SOWE
% \tkzgr@relative{<name>}{<x factor>}{<y factor>}
%<--------------------------------------------------------------------------->
\def\tkzgr@relative#1#2#3{%
  \expandafter\newcommand\expandafter*\csname tkzgr@#1\endcsname[1][]{%
    \csname tkzgr@@#1\endcsname[##1]}%
  \expandafter\def\csname tkzgr@@#1\endcsname[##1](##2)##3{%
    \begingroup
      \tkzgr@setkeys{vertex}{##1}%
      \path (##2)--++(#2\cmdGR@vertex@unit,#3\cmdGR@vertex@unit)
            coordinate (##3);
      \tkzgr@Vertex[##1,Node]{##3}
    \endgroup}}
\tkzgr@relative{EA}{}{0*}
\tkzgr@relative{WE}{-}{0*}
\tkzgr@relative{NO}{0*}{}
\tkzgr@relative{SO}{0*}{-}
\tkzgr@relative{NOEA}{}{}
\tkzgr@relative{NOWE}{-}{}
\tkzgr@relative{SOEA}{}{-}
\tkzgr@relative{SOWE}{-}{-}
%<--------------------------------------------------------------------------->
%                               Vertices
%<--------------------------------------------------------------------------->
% \Vertices[options]{form}{list} ; form : line, square, tr1, tr2, tr3, tr4,
% circle ; each form is the macro \tkzgr@vertices@<form>
\newcommand*{\tkzgr@Vertices}[1][]{\tkzgr@vertices@nostar[#1]}%
\def\tkzgr@vertices@nostar[#1]#2#3{%
\tkzgr@setkeys{vertex}{#1}%
\begingroup%
   \setcounter{tkz@gr@p}{0}%
   \@for\tkzgr@liste:=#3\do{%
     \stepcounter{tkz@gr@p}%
     \global\expandafter\let\csname label@\alph{tkz@gr@p}\endcsname
                                \tkzgr@liste}%
   \@ifundefined{tkzgr@vertices@#2}%
     {\PackageWarning{tkz-graph}{Unknown form `#2' for \string\Vertices}}%
     {\csname tkzgr@vertices@#2\endcsname{#1}{#3}}%
\endgroup%
}
\def\tkzgr@vertices@line#1#2{%
   \setcounter{tkz@gr@p}{0}%
   \foreach \tkzgr@fin in {#2}{%
       \ifnum\value{tkz@gr@p}=0
       \global\let\tkzgr@deb\tkzgr@fin
       \tkzgr@Vertex[#1]{\tkzgr@fin}
       \stepcounter{tkz@gr@p}
       \else
       \cmdGR@vertex@dir[#1,x={},y={},a={},d={},Node=false]%
                        (\tkzgr@deb){\tkzgr@fin}
       \global\let\tkzgr@deb\tkzgr@fin
       \fi
     }}
\def\tkzgr@vertices@square#1#2{%
     \begin{scope}[rotate=45]
       \tkzgr@Vertex[#1,Lpos=-135]{\label@a}
        \tkzgr@EA[#1,Lpos=-45,x={},y={},Node=false](\label@a){\label@b}
        \tkzgr@NO[#1,Lpos=45, x={},y={},Node=false](\label@b){\label@c}
        \tkzgr@WE[#1,Lpos=135,x={},y={},Node=false](\label@c){\label@d}
     \end{scope}}
\def\tkzgr@vertices@tri#1#2#3{%
     \tkzgr@Vertex[#1]{\label@a}
     #2[#1,x={},y={},Node=false](\label@a){\label@b}
     #3[#1,x={},y={},Node=false](\label@b){\label@c}}
\def\tkzgr@vertices@trI#1#2{\tkzgr@vertices@tri{#1}\tkzgr@EA\tkzgr@NO}
\def\tkzgr@vertices@trII#1#2{\tkzgr@vertices@tri{#1}\tkzgr@NO\tkzgr@EA}
\def\tkzgr@vertices@trIII#1#2{\tkzgr@vertices@tri{#1}\tkzgr@NO\tkzgr@WE}
\def\tkzgr@vertices@trIV#1#2{\tkzgr@vertices@tri{#1}\tkzgr@WE\tkzgr@NO}
\expandafter\let\csname tkzgr@vertices@tr1\endcsname\tkzgr@vertices@trI
\expandafter\let\csname tkzgr@vertices@tr2\endcsname\tkzgr@vertices@trII
\expandafter\let\csname tkzgr@vertices@tr3\endcsname\tkzgr@vertices@trIII
\expandafter\let\csname tkzgr@vertices@tr4\endcsname\tkzgr@vertices@trIV
% keys rotation (angle of the first vertex) and clockwise
\def\tkzgr@turn{%
  \ifGR@vertex@clockwise
    \pgfmathparse{\cmdGR@vertex@rotation-\tkzgr@newangle}%
    \let\tkzgr@newangle\pgfmathresult
  \else
    \pgfmathparse{\cmdGR@vertex@rotation}%
    \ifdim\pgfmathresult pt=\z@\else
      \pgfmathparse{\cmdGR@vertex@rotation+\tkzgr@newangle}%
      \let\tkzgr@newangle\pgfmathresult
    \fi
  \fi}
\def\tkzgr@vertices@circle#1#2{%
    \pgfmathdivide{360}{\value{tkz@gr@p}}%
    \global\let\tkzgr@angle\pgfmathresult%
    \setcounter{tkz@gr@p}{0}%
    \foreach \tkzgr@lab in {#2}{%
      \pgfmathmultiply{\tkzgr@angle}{\thetkz@gr@p}%
      \let\tkzgr@newangle\pgfmathresult%
      \tkzgr@turn
      \pgfmathadd{\cmdGR@vertex@Lpos}{\tkzgr@newangle}%
      \let\tkzgr@posangle\pgfmathresult%
        \tkzgr@Vertex[#1,
              a    = \tkzgr@newangle,
              d    = \cmdGR@vertex@unit,
              Lpos = \tkzgr@posangle]{\tkzgr@lab}
          \stepcounter{tkz@gr@p}%
      }}
%<--------------------------------------------------------------------------->
%                          Edge style
%<--------------------------------------------------------------------------->
\tikzset{LabelStyle/.style={}}% add 03/04/2009
\tikzset{EdgeStyle/.style={}}
%<--------------------------------------------------------------------------->
%                          Init    SetUpEdge
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{SUE}{color}
\tkzgr@cmdkey{SUE}{label}
\tkzgr@cmdkey{SUE}{labelstyle}
\tkzgr@cmdkey{SUE}{labeltext}
\tkzgr@cmdkey{SUE}{labelcolor}
\tkzgr@cmdkey{SUE}{style}
\tkzgr@cmdkey{SUE}{lw}
\tkzgr@presetkeys{SUE}{color        = \EdgeColor,
                       lw           = \EdgeLineWidth,
                       label        = {},
                       labeltext    = \LabelTextColor,
                       labelcolor   = \LabelFillColor,
                       labelstyle   = {},
                       style        = {}}
%<--------------------------------------------------------------------------->
%                             SetUpEdge
%<--------------------------------------------------------------------------->
\newcommand*{\SetUpEdge}[1][]{\tkzgr@SetUpEdge[#1]}%
\def\tkzgr@SetUpEdge[#1]{%
\tkzgr@setkeys{SUE}{#1}%
\tkzgr@presetkeys{edge}{color        = \cmdGR@SUE@color,
                        lw           = \cmdGR@SUE@lw,
                        label        = \cmdGR@SUE@label,
                        labeltext    = \cmdGR@SUE@labeltext,
                        labelcolor   = \cmdGR@SUE@labelcolor,
                        labelstyle   = \cmdGR@SUE@labelstyle,
                        style        = \cmdGR@SUE@style}
\tikzset{LabelStyle/.style={}}
\tikzset{EdgeStyle/.style={}}}
\newcommand*{\DisableEdgeStyle}{\tikzset{EdgeStyle/.style={}}}
%<--------------------------------------------------------------------------->
%                              Init Edge
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{edge}{color}
\tkzgr@cmdkey{edge}{lw}
\tkzgr@cmdkey{edge}{double}
\tkzgr@cmdkey{edge}{incolor}
\tkzgr@cmdkey{edge}{dd}
\tkzgr@cmdkey{edge}{style}
\tkzgr@cmdkey{edge}{label}
\tkzgr@cmdkey{edge}{labeltext}
\tkzgr@cmdkey{edge}{labelcolor}
\tkzgr@cmdkey{edge}{labelstyle}
\tkzgr@boolkey{edge}{local}
% arrows : arrow = <tikz arrow> or the short keys ->, <-, <->, -
\tkzgr@cmdkey{edge}{arrow}
\pgfkeys{/tkzgraph/edge/->/.style  = {/tkzgraph/edge/arrow = ->},
         /tkzgraph/edge/<-/.style  = {/tkzgraph/edge/arrow = <-},
         /tkzgraph/edge/<->/.style = {/tkzgraph/edge/arrow = <->},
         /tkzgraph/edge/-/.style   = {/tkzgraph/edge/arrow = {}}}
\tkzgr@presetkeys{edge}{style      = {pos=.5},
                        lw         = \EdgeLineWidth,
                        label      = {},
                        labeltext  = \LabelTextColor,
                        labelcolor = \LabelFillColor,
                        labelstyle = {},
                        local      = false,
                        double     = {},
                        dd         = \EdgeDoubleDistance,
                        incolor    = \EdgeFillColor,
                        color      = \EdgeColor,
                        arrow      = {}}
%<--------------------------------------------------------------------------->
%                               Edge
%<--------------------------------------------------------------------------->
\newcommand*{\tkzgr@Edge}[1][]{\tkzgr@edge[#1]}%
\def\tkzgr@edge[#1](#2)(#3){%
\tkzgr@setkeys{edge}{#1}%
\tkzgr@recordedge{#2}{#3}%
 \begingroup%
\tkzgr@ifempty{\cmdGR@edge@arrow}%
  {\let\tkzgr@arrowopts\@empty}%
  {\edef\tkzgr@arrowopts{,\cmdGR@edge@arrow,>={\tkzgr@arrowtip}}}%
\tkzgr@ifempty{\cmdGR@edge@double}{%
\tikzset{LocalEdgeStyle/.style={color = \cmdGR@edge@color,
                                line width = \cmdGR@edge@lw}}}{%
\tikzset{LocalEdgeStyle/.style={line width = \cmdGR@edge@dd,
                                color = \cmdGR@edge@double,
                                double distance = \cmdGR@edge@lw,
                                double  = \cmdGR@edge@color}}}%
\ifGR@edge@local%
      \tikzset{EdgeStyle/.style={}}%
      \fi
   \tkzgr@ifempty{\cmdGR@edge@label}{%
     \protected@edef\@tempa{%
     \noexpand   \draw[LocalEdgeStyle,\cmdGR@edge@style,EdgeStyle\tkzgr@arrowopts]}%
                 \@tempa (#2) to (#3)}{%
     \protected@edef\@tempa{%
     \noexpand   \draw[LocalEdgeStyle,\cmdGR@edge@style,EdgeStyle\tkzgr@arrowopts] (#2) to%
    node[fill = \cmdGR@edge@labelcolor,
         text = \cmdGR@edge@labeltext,
         \cmdGR@edge@labelstyle,LabelStyle]}\@tempa
   {\cmdGR@edge@label} (#3)}%
   ;
\endgroup%
}%
%<--------------------------------------------------------------------------->
%                               Edges
%<--------------------------------------------------------------------------->
\newcommand*{\tkzgr@Edges}[1][]{\tkzgr@edges[#1]}%
\def\tkzgr@edges[#1](#2){%
\tkzgr@setkeys{edge}{#1}%
 \begingroup%
   \setcounter{tkz@gr@p}{0}%
   \foreach \tkzgr@fin in {#2}{%
       \ifnum\value{tkz@gr@p}=0
       \global\let\tkzgr@deb\tkzgr@fin
       \stepcounter{tkz@gr@p}%
       \else
       \tkzgr@Edge[#1](\tkzgr@deb)(\tkzgr@fin)
       \global\let\tkzgr@deb\tkzgr@fin
       \fi
   }
 \endgroup%
}%
%<--------------------------------------------------------------------------->
%                          Init  loop
%<--------------------------------------------------------------------------->
\tkzgr@choicekey{loop}{dir}{WE,EA,NO,SO,NOWE,NOEA,SOWE,SOEA}{%
\ifcase\nr\relax
\tikzset{LoopStyle/.style = {in=225, out=135, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in= 45, out=-45, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in=135, out= 45, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in=-45, out=-135, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in=180, out=90, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in=90, out=0, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in=-90, out=-180, distance=\cmdGR@loop@dist}}%
\or
\tikzset{LoopStyle/.style = {in=0, out=-90, distance=\cmdGR@loop@dist}}%
\fi%
}
\tkzgr@cmdkey{loop}{color}
\tkzgr@cmdkey{loop}{label}
\tkzgr@cmdkey{loop}{labelstyle}
\tkzgr@cmdkey{loop}{style}
\tkzgr@cmdkey{loop}{dist}
\tkzgr@presetkeys{loop}{style      = {pre,thick},%`
                        label      = {},%
                        labelstyle = {},%
                        color      = \tkz@suc@txt,%
                        dist       = 4cm,%
                        dir        = WE}
%<--------------------------------------------------------------------------->
%                                loop
%<--------------------------------------------------------------------------->
\newcommand*{\grLoop}[1][]{\tkzgr@loop[#1]}%
\newcommand*{\tkzgr@Loop}[1][]{\tkzgr@loop[#1]}%
\def\tkzgr@loop[#1](#2){%
\tkzgr@setkeys{loop}{#1}%
\tkzgr@recordedge{#2}{#2}%
\protected@edef\@tempa{%
\noexpand \draw[\cmdGR@loop@color] (#2)%
  edge [EdgeStyle,LoopStyle,\cmdGR@loop@style]%
  node [LabelStyle,\cmdGR@loop@labelstyle]%
  {\cmdGR@loop@label} (#2)}\@tempa;%
}%
%<--------------------------------------------------------------------------->
%                    Init   Graphes probabilistes
%<--------------------------------------------------------------------------->
\tkzgr@cmdkey{grpb}{unit}
\tkzgr@cmdkey{grpb}{LposA}
\tkzgr@cmdkey{grpb}{LposB}
\tkzgr@cmdkey{grpb}{Ldist}
\tkzgr@cmdkey{grpb}{LoopDist}
\tkzgr@presetkeys{grpb}{LposA    = 180,%
                        LposB    = 0,%
                        Ldist    = 0cm,%
                        LoopDist = 4cm,
                        unit     = 4}
%<--------------------------------------------------------------------------->
%                       Graphes probabilistes
%<--------------------------------------------------------------------------->
\newcommand*{\grProb}[7][]{%
\tkzgr@setkeys{grpb}{#1}%
\tikzset{LabelStyle/.append style ={pos=.5}}
\tkzgr@Vertex[Lpos=\cmdGR@grpb@LposA,Ldist=\cmdGR@grpb@Ldist,L=#2]{grA}
\tkzgr@EA[unit=\cmdGR@grpb@unit,Lpos=\cmdGR@grpb@LposB,
    Ldist=\cmdGR@grpb@Ldist,L=#3](grA){grB}
\tkzgr@Edge[style={post,bend left=60},label={$#4$},labelstyle={above}](grA)(grB)
\tkzgr@Edge[style={post,bend left=60},label={$#5$},labelstyle={below}](grB)(grA)
\tkzgr@Loop[dist=\cmdGR@grpb@LoopDist,dir=WE,label={$#6$},labelstyle={left}](grA)
\tkzgr@Loop[dist=\cmdGR@grpb@LoopDist,dir=EA,label={$#7$},labelstyle={right}](grB)
}%
\newcommand*{\grProbThree}[7][]{%
\tkzgr@setkeys{grpb}{#1}%
\begin{scope}[]
  \tikzset{LabelStyle/.append style ={pos=.5}}
  \tkzgr@Vertices[empty,unit=\cmdGR@grpb@unit]{circle}{grA,grB,grC}
   \tkzgr@Vertex[Node,Lpos=\cmdGR@grpb@LposA,Ldist=\cmdGR@grpb@Ldist,L=#2]{grA}
   \tkzgr@Vertex[Node,Lpos=\cmdGR@grpb@LposA,Ldist=\cmdGR@grpb@Ldist,L=#3]{grB}
   \tkzgr@Vertex[Node,Lpos=\cmdGR@grpb@LposA,Ldist=\cmdGR@grpb@Ldist,L=#4]{grC}
   \foreach \tkzgr@x/\tkzgr@y/\tkzgr@z in {#5} {%
   \tkzgr@Loop[dist=\cmdGR@grpb@LoopDist,dir=EA,label={$\tkzgr@x$}](grA)
\tkzgr@Edge[style={post,bend right=20},label={$\tkzgr@y$}](grA)(grB)
\tkzgr@Edge[style={post,bend right=20},label={$\tkzgr@z$}](grA)(grC)}
\foreach \tkzgr@x/\tkzgr@y/\tkzgr@z in {#6} {%
   \tkzgr@Loop[dist=\cmdGR@grpb@LoopDist,dir=NO,label={$\tkzgr@x$}](grB)
\tkzgr@Edge[style={post,bend right=20},label={$\tkzgr@y$}](grB)(grA)
\tkzgr@Edge[style={post,bend right=20},label={$\tkzgr@z$}](grB)(grC)}
   \foreach \tkzgr@x/\tkzgr@y/\tkzgr@z in {#7} {%
   \tkzgr@Loop[dist=\cmdGR@grpb@LoopDist,dir=SO,label={$\tkzgr@x$}](grC)
 \tkzgr@Edge[style={post,bend right=20},label={$\tkzgr@y$}](grC)(grA)
 \tkzgr@Edge[style={post,bend right=20},label={$\tkzgr@z$}](grC)(grB)}
\end{scope}
}
%<--------------------------------------------------------------------------->
%                      End   Graphes probabilistes
%<--------------------------------------------------------------------------->
\newcommand{\SetVertexLabeledSmall}{%
\SetVertexLabel%
\tikzset{VertexStyle/.style = {draw,
                               shape           = circle,
                               inner sep       = 1pt,
                               minimum size    = 10pt}}
\tikzset{EdgeStyle/.style  = {double           = \tkz@suc@txt,
                              double distance  = 1pt,
                              color            = \tkz@suc@bkc,
                              line width       = 0.7pt}}
}
\newcommand{\SetVertexNotLabeledSmall}{%
  \tikzset{EdgeStyle/.style = {double = \tkz@suc@txt,
                               double distance = 1pt,
                               color = \tkz@suc@bkc,
                               line width = 0.7pt}}
  \SetVertexNoLabel
  \SetVertexSimple[MinSize=6pt,FillColor=gray]
  \renewcommand*{\VertexLineWidth}{0pt}
}%

\newcommand{\SetVertexForPresentation}[3]{%
  \GraphInit[vstyle=Shade]
  \SetVertexNoLabel
  \renewcommand*{\VertexBigMinSize}{12pt}%
  \renewcommand*{\EdgeDoubleDistance}{2pt}%
  \renewcommand*{\EdgeLineWidth}{0.7pt}%
  \SetGraphShadeColor{#1}{#2}{#3}
}%

\newcommand{\setxyzvec}[1][20]{%
  \pgfmathsetmacro{\xone}{cos(180+#1)}%
  \pgfmathsetmacro{\yone}{sin(180+#1)}%
  \pgfmathsetmacro{\xtwo}{cos(360-#1)}%
  \pgfmathsetmacro{\ytwo}{sin(360-#1)}%
  \pgfsetxvec{\pgfpoint{\xone cm}{\yone cm}}%
  \pgfsetyvec{\pgfpoint{\xtwo cm}{\ytwo cm}}%
  \pgfsetzvec{\pgfpoint{0cm}{1cm}}%
}
%<--------------------------------------------------------------------------->
%                    \tkzSetUpGraph : global settings
%<--------------------------------------------------------------------------->
% Each key changes one of the macros \Vertex..., \Edge..., \Label...,
% \GraphUnit (the old way was \renewcommand). The changes are local :
% inside a group or a tikzpicture they stop at the end of it.
% directed : every edge gets an arrow (key -> of \Edge) ; directed=false
% cancels it. arrow tip : the tip used by the keys ->, <-, <-> of \Edge
% (stealth' by default ; for the tips Stealth, Latex ... load the
% library arrows.meta : it is not loaded by tkz-graph because it changes
% slightly the default tip "to").
\def\tkzgr@arrowtip{stealth'}
\def\tkzgr@true{true}
\def\tkzgr@directed#1{%
  \edef\tkzgr@tmpd{#1}%
  \ifx\tkzgr@tmpd\tkzgr@true
    \tkzgr@presetkeys{edge}{arrow = ->}%
  \else
    \tkzgr@presetkeys{edge}{arrow = {}}%
  \fi}
\pgfkeys{/tkzgraph/setup/.cd,
  vertex shape/.code         = {\def\VertexShape{#1}},
  vertex line width/.code    = {\def\VertexLineWidth{#1}},
  vertex line color/.code    = {\def\VertexLineColor{#1}},
  vertex text color/.code    = {\def\VertexTextColor{#1}},
  vertex fill/.code          = {\def\VertexFillColor{#1}},
  light fill/.code           = {\def\VertexLightFillColor{#1}},
  dark fill/.code            = {\def\VertexDarkFillColor{#1}},
  ball color/.code           = {\def\VertexBallColor{#1}},
  inner sep/.code            = {\def\VertexInnerSep{#1}},
  outer sep/.code            = {\def\VertexOuterSep{#1}},
  small size/.code           = {\def\VertexSmallMinSize{#1}},
  medium size/.code          = {\def\VertexInterMinSize{#1}},
  big size/.code             = {\def\VertexBigMinSize{#1}},
  edge color/.code           = {\def\EdgeColor{#1}},
  edge width/.code           = {\def\EdgeLineWidth{#1}},
  edge fill/.code            = {\def\EdgeFillColor{#1}},
  art color/.code            = {\def\EdgeArtColor{#1}},
  double distance/.code      = {\def\EdgeDoubleDistance{#1}},
  label text/.code           = {\def\LabelTextColor{#1}},
  label fill/.code           = {\def\LabelFillColor{#1}},
  unit/.code                 = {\def\GraphUnit{#1}},
  directed/.code             = {\tkzgr@directed{#1}},
  directed/.default          = true,
  arrow tip/.code            = {\def\tkzgr@arrowtip{#1}}}
\newcommand*{\tkzSetUpGraph}[1][]{\pgfqkeys{/tkzgraph/setup}{#1}}
%<--------------------------------------------------------------------------->
%                    Recording of the graph (vertices, edges)
%<--------------------------------------------------------------------------->
% Each tikzpicture starts a new record. \tkzgr@vlist : names of the
% vertices in order of creation ; \tkzgr@elist : edges A/B (a loop is A/A).
% Used by \tkzAdjacencyMatrix.
\def\tkzgr@resetrecord{\global\let\tkzgr@vlist\@empty
                       \global\let\tkzgr@elist\@empty}
\tkzgr@resetrecord
\def\tkzgr@recordvertex#1{%
  \protected@edef\tkzgr@vn{#1}%
  \edef\tkzgr@tmp{\noexpand\in@{,\tkzgr@vn,}{,\tkzgr@vlist,}}%
  \tkzgr@tmp
  \ifin@\else
    \xdef\tkzgr@vlist{\ifx\tkzgr@vlist\@empty\else\tkzgr@vlist,\fi
                      \tkzgr@vn}%
  \fi}
\def\tkzgr@recordedge#1#2{%
  \protected@edef\tkzgr@vn{#1/#2}%
  \xdef\tkzgr@elist{\ifx\tkzgr@elist\@empty\else\tkzgr@elist,\fi
                    \tkzgr@vn}}
%<--------------------------------------------------------------------------->
%                         \tkzHighlightPath
%<--------------------------------------------------------------------------->
% \tkzHighlightPath[options]{A,B,C,D}  path A-B-C-D drawn again over the
%                                      edges (cycle : D-A added)
% \tkzHighlightPath[options]{A/B,C/D}  edges A-B and C-D
% options : color (red), lw (1.6pt), style (tikz options, for example
% bend left=20 to follow a bent edge), cycle
\tkzgr@cmdkey{hl}{color}
\tkzgr@cmdkey{hl}{lw}
\tkzgr@cmdkey{hl}{style}
\tkzgr@boolkey{hl}{cycle}
\tkzgr@presetkeys{hl}{color = red,
                      lw    = 1.6pt,
                      style = {},
                      cycle = false}
\newcommand*{\tkzHighlightPath}[2][]{%
\begingroup
  \tkzgr@setkeys{hl}{#1}%
  \in@{/}{#2}%
  \ifin@
    \foreach \tkzgr@ha/\tkzgr@hb in {#2}{\tkzgr@hledge{\tkzgr@ha}{\tkzgr@hb}}%
  \else
    \setcounter{tkz@gr@p}{0}%
    \foreach \tkzgr@fin in {#2}{%
      \ifnum\value{tkz@gr@p}=0
        \global\let\tkzgr@first\tkzgr@fin
        \stepcounter{tkz@gr@p}%
      \else
        \tkzgr@hledge{\tkzgr@deb}{\tkzgr@fin}%
      \fi
      \global\let\tkzgr@deb\tkzgr@fin}%
    \ifGR@hl@cycle\tkzgr@hledge{\tkzgr@deb}{\tkzgr@first}\fi
  \fi
\endgroup}
\def\tkzgr@hledge#1#2{%
  \protected@edef\@tempa{\noexpand\draw[color = \cmdGR@hl@color,
                                        line width = \cmdGR@hl@lw,
                                        \cmdGR@hl@style] (#1) to (#2)}%
  \@tempa;}
%<--------------------------------------------------------------------------->
%                        Adjacency matrix
%<--------------------------------------------------------------------------->
% \tkzAdjacencyMatrix[options] : matrix of the graph of the last
% tikzpicture (math mode or not). Entry (i,j) : number of edges between
% the i-th and the j-th vertex (a loop counts 1).
% options : directed (edge A-B counts only for (A,B)),
%           order = {A,B,...} (default : order of creation)
\newcount\tkzgr@cnt
\tkzgr@boolkey{adj}{directed}
\tkzgr@cmdkey{adj}{order}
\tkzgr@presetkeys{adj}{directed = false,
                       order    = {}}
% \tkzgr@countedges{i}{j} -> \tkzgr@cnt
\def\tkzgr@countedges#1#2{%
  \tkzgr@cnt\z@
  \edef\tkzgr@i{#1}\edef\tkzgr@j{#2}%
  \@for\tkzgr@e:=\tkzgr@elist\do{%
    \ifx\tkzgr@e\@empty\else
      \expandafter\tkzgr@cmpedge\tkzgr@e\@nil
    \fi}}
\def\tkzgr@cmpedge#1/#2\@nil{%
  \def\tkzgr@u{#1}\def\tkzgr@v{#2}%
  \ifx\tkzgr@u\tkzgr@i
    \ifx\tkzgr@v\tkzgr@j\advance\tkzgr@cnt\@ne\fi
  \else
    \ifGR@adj@directed\else
      \ifx\tkzgr@u\tkzgr@j
        \ifx\tkzgr@v\tkzgr@i\advance\tkzgr@cnt\@ne\fi
      \fi
    \fi
  \fi}
\newcommand*{\tkzAdjacencyMatrix}[1][]{%
\begingroup
  \tkzgr@setkeys{adj}{#1}%
  \tkzgr@ifempty{\cmdGR@adj@order}%
    {\let\tkzgr@order\tkzgr@vlist}%
    {\edef\tkzgr@order{\cmdGR@adj@order}}%
  \global\let\tkzgr@rows\@empty
  \global\let\tkzgr@cols\@empty
  \foreach \tkzgr@a in \tkzgr@order {%
    \xdef\tkzgr@cols{\tkzgr@cols c}%
    \global\let\tkzgr@row\@empty
    \foreach \tkzgr@b in \tkzgr@order {%
      \tkzgr@countedges{\tkzgr@a}{\tkzgr@b}%
      \xdef\tkzgr@row{\ifx\tkzgr@row\@empty\else\tkzgr@row&\fi
                      \the\tkzgr@cnt}}%
    \xdef\tkzgr@rows{\ifx\tkzgr@rows\@empty\else
                       \unexpanded\expandafter{\tkzgr@rows}\noexpand\\\fi
                     \tkzgr@row}}%
  \edef\tkzgr@tmp{\noexpand\left(\noexpand\begin{array}{\tkzgr@cols}%
     \unexpanded\expandafter{\tkzgr@rows}\noexpand\end{array}\noexpand\right)}%
  \ensuremath{\tkzgr@tmp}%
\endgroup}
%<--------------------------------------------------------------------------->
%                       Graph from a matrix
%<--------------------------------------------------------------------------->
% \tkzGraphFromMatrix[options]{A,B,C}{0,1,1;1,0,1;1,1,0}
% rows separated by ; entries by , (decimal point : .)
% A non-zero entry (i,j) gives an edge (i,j) ; on the diagonal a loop.
% options :
%  placed        the vertices already exist (otherwise they are drawn
%                on a circle, as \Vertices{circle})
%  unit, rotation, clockwise   for the circle
%  directed      arrows ; edges i->j and j->i are bent
%  weighted      the entries are written on the edges
%  style         tikz options added to each edge
%  loop distance size of the loops (1cm)
%  bend          angle used for the pairs i->j, j->i (15)
\tkzgr@boolkey{mat}{placed}
\tkzgr@boolkey{mat}{directed}
\tkzgr@boolkey{mat}{weighted}
\tkzgr@boolkey{mat}{clockwise}
\tkzgr@cmdkey{mat}{unit}
\tkzgr@cmdkey{mat}{rotation}
\tkzgr@cmdkey{mat}{style}
\tkzgr@cmdkey{mat}{loopdist}
\pgfkeys{/tkzgraph/mat/loop distance/.style = {/tkzgraph/mat/loopdist = #1}}
\tkzgr@cmdkey{mat}{bend}
\tkzgr@presetkeys{mat}{placed        = false,
                       directed      = false,
                       weighted      = false,
                       clockwise     = false,
                       unit          = \GraphUnit,
                       rotation      = 0,
                       style         = {},
                       loopdist      = 1cm,
                       bend          = 15}
\newcount\tkzgr@mi
\newcount\tkzgr@mj
\newcount\tkzgr@mn
\newcommand*{\tkzGraphFromMatrix}[3][]{%
\begingroup
  \tkzgr@setkeys{mat}{#1}%
  % names : \tkzgr@m@name@<i>
  \tkzgr@mn\z@
  \@for\tkzgr@a:=#2\do{%
    \advance\tkzgr@mn\@ne
    \expandafter\let\csname tkzgr@m@name@\the\tkzgr@mn\endcsname\tkzgr@a}%
  % entries : \tkzgr@m@<i>@<j>
  \tkzgr@mi\z@
  \tkzgr@rowsloop#3;\relax;%
  % vertices
  \ifGR@mat@placed\else
    \edef\tkzgr@tmp{\noexpand\tkzgr@Vertices[unit = \cmdGR@mat@unit,
                    rotation = \cmdGR@mat@rotation,
                    clockwise = \ifGR@mat@clockwise true\else false\fi]%
                    {circle}{#2}}%
    \tkzgr@tmp
  \fi
  \tkzgr@centroid
  % edges and loops
  \tkzgr@mi\z@
  \loop\ifnum\tkzgr@mi<\tkzgr@mn
    \advance\tkzgr@mi\@ne
    {\tkzgr@mj\z@
     \loop\ifnum\tkzgr@mj<\tkzgr@mn
       \advance\tkzgr@mj\@ne
       \tkzgr@matentry
     \repeat}%
  \repeat
\endgroup}
% one row : #1 = 0,1,1
\def\tkzgr@rowsloop#1;{%
  \ifx\relax#1\else
    \advance\tkzgr@mi\@ne
    \tkzgr@mj\z@
    \@for\tkzgr@a:=#1\do{%
      \advance\tkzgr@mj\@ne
      \expandafter\let
        \csname tkzgr@m@\the\tkzgr@mi @\the\tkzgr@mj\endcsname\tkzgr@a}%
    \expandafter\tkzgr@rowsloop
  \fi}
% \tkzgr@ifnonzero{value}{true}{false}
\def\tkzgr@ifnonzero#1{%
  \tkzgr@ifempty{#1}{\@secondoftwo}{%
    \pgfmathparse{(#1)!=0}%
    \ifdim\pgfmathresult pt>\z@
      \expandafter\@firstoftwo
    \else
      \expandafter\@secondoftwo
    \fi}}
\def\tkzgr@mval#1#2{\csname tkzgr@m@#1@#2\endcsname}
\def\tkzgr@mname#1{\csname tkzgr@m@name@#1\endcsname}
% centre of the vertices -> \tkzgr@cx, \tkzgr@cy (pt)
\def\tkzgr@centroid{%
  \def\tkzgr@cx{0}\def\tkzgr@cy{0}%
  \tkzgr@mi\z@
  \loop\ifnum\tkzgr@mi<\tkzgr@mn
    \advance\tkzgr@mi\@ne
    \pgfextractx{\pgf@xa}{\pgfpointanchor{\tkzgr@mname{\the\tkzgr@mi}}{center}}%
    \pgfextracty{\pgf@ya}{\pgfpointanchor{\tkzgr@mname{\the\tkzgr@mi}}{center}}%
    \pgfmathsetmacro\tkzgr@cx{\tkzgr@cx+\pgf@xa/\the\tkzgr@mn}%
    \pgfmathsetmacro\tkzgr@cy{\tkzgr@cy+\pgf@ya/\the\tkzgr@mn}%
  \repeat}
% entry (\tkzgr@mi,\tkzgr@mj)
\def\tkzgr@matentry{%
  \edef\tkzgr@v{\tkzgr@mval{\the\tkzgr@mi}{\the\tkzgr@mj}}%
  \tkzgr@ifnonzero{\tkzgr@v}{%
    \ifnum\tkzgr@mi=\tkzgr@mj
      \tkzgr@matloop
    \else
      \ifGR@mat@directed
        \tkzgr@matedge
      \else
        \ifnum\tkzgr@mi<\tkzgr@mj\tkzgr@matedge\fi
      \fi
    \fi}{}}
\def\tkzgr@matedge{%
  \def\tkzgr@bend{}%
  \ifGR@mat@directed
    \edef\tkzgr@w{\tkzgr@mval{\the\tkzgr@mj}{\the\tkzgr@mi}}%
    \tkzgr@ifnonzero{\tkzgr@w}{\edef\tkzgr@bend{bend left=\cmdGR@mat@bend}}{}%
  \fi
  \edef\tkzgr@tmp{\noexpand\tkzgr@Edge[%
      \ifGR@mat@directed ->,\fi
      \ifGR@mat@weighted label = {$\tkzgr@v$},\fi
      style = {\tkzgr@bend,\unexpanded\expandafter{\cmdGR@mat@style}}]%
      (\tkzgr@mname{\the\tkzgr@mi})(\tkzgr@mname{\the\tkzgr@mj})}%
  \tkzgr@tmp}
% loop directed away from the centre
\def\tkzgr@matloop{%
  \edef\tkzgr@n{\tkzgr@mname{\the\tkzgr@mi}}%
  \pgfextractx{\pgf@xa}{\pgfpointanchor{\tkzgr@n}{center}}%
  \pgfextracty{\pgf@ya}{\pgfpointanchor{\tkzgr@n}{center}}%
  \pgfmathsetmacro\tkzgr@dx{\pgf@xa-\tkzgr@cx}%
  \pgfmathsetmacro\tkzgr@dy{\pgf@ya-\tkzgr@cy}%
  \pgfmathsetmacro\tkzgr@th{%
     (abs(\tkzgr@dx)+abs(\tkzgr@dy)<0.01) ? 90 : atan2(\tkzgr@dy,\tkzgr@dx)}%
  \tkzgr@recordedge{\tkzgr@n}{\tkzgr@n}%
  \protected@edef\@tempa{\noexpand\draw[EdgeStyle,
      color = \EdgeColor, line width = \EdgeLineWidth,
      \ifGR@mat@directed ->, >={\tkzgr@arrowtip},\fi
      \cmdGR@mat@style]
    (\tkzgr@n) to[out = \tkzgr@th+35, in = \tkzgr@th-35,
                  distance = \cmdGR@mat@loopdist]
    \ifGR@mat@weighted
      node[fill = \LabelFillColor, text = \LabelTextColor, LabelStyle]
          {$\tkzgr@v$}%
    \fi
    (\tkzgr@n)}%
  \@tempa;}
% probabilistic graph : weighted and directed graph from the matrix
% of transition
\newcommand*{\grProbMatrix}[3][]{%
  \tkzGraphFromMatrix[directed,weighted,#1]{#2}{#3}}
%<--------------------------------------------------------------------------->
%                       Short names and prefixed names
%<--------------------------------------------------------------------------->
% The code uses only \tkzgr@<name>. The prefixed names \tkz<name> are
% always defined. The short names \<name> are installed
%  - at the loading of the package, only if they are not defined
%    (otherwise a warning) ;
%  - at the beginning of each tikzpicture (local definitions, so a
%    user definition of \EA, \NO ... is restored after the picture).
% With the option noshortnames, the short names are never defined.
\def\tkzgr@shortlist{Vertex,Vertices,Edge,Edges,Loop,%
                     EA,WE,NO,SO,NOEA,NOWE,SOEA,SOWE}
\@for\tkzgr@n:=\tkzgr@shortlist\do{%
  \expandafter\let\csname tkz\tkzgr@n\expandafter\endcsname
                  \csname tkzgr@\tkzgr@n\endcsname}
\def\tkzgr@shortnames{%
  \let\Vertex\tkzgr@Vertex
  \let\Vertices\tkzgr@Vertices
  \let\Edge\tkzgr@Edge
  \let\Edges\tkzgr@Edges
  \let\Loop\tkzgr@Loop
  \let\EA\tkzgr@EA
  \let\WE\tkzgr@WE
  \let\NO\tkzgr@NO
  \let\SO\tkzgr@SO
  \let\NOEA\tkzgr@NOEA
  \let\NOWE\tkzgr@NOWE
  \let\SOEA\tkzgr@SOEA
  \let\SOWE\tkzgr@SOWE}
\iftkzgr@short
  \@for\tkzgr@n:=\tkzgr@shortlist\do{%
    \@ifundefined{\tkzgr@n}{%
      \expandafter\let\csname\tkzgr@n\expandafter\endcsname
                      \csname tkzgr@\tkzgr@n\endcsname}{%
      \PackageWarningNoLine{tkz-graph}{\expandafter\string
        \csname\tkzgr@n\endcsname\space is already defined. Inside the
        tikzpicture environments it is replaced by the command of
        tkz-graph ; outside, use \expandafter\string
        \csname tkz\tkzgr@n\endcsname}}}
  \ifdefined\AddToHook
    \AddToHook{env/tikzpicture/begin}{\tkzgr@shortnames}
  \else
    \tikzset{every picture/.append style={%
      execute at begin picture=\tkzgr@shortnames}}
  \fi
\fi
% new record of the graph at the beginning of each picture
\ifdefined\AddToHook
  \AddToHook{env/tikzpicture/begin}{\tkzgr@resetrecord}
\else
  \tikzset{every picture/.append style={%
    execute at begin picture=\tkzgr@resetrecord}}
\fi
\endinput