Central Functions of Rank 1-3

Snippets Page

Central functions of ranks 1-3, and arbitrary rank.

Source Code

% rank one
    \tikz[trivalent]{
        \draw(0,.5)circle(.5);
        \node[basiclabel]at(.5,1){$c$};
        \node[small matrix]at(-.5,.5){$\mathbf{X}$};
    }
% rank two
    \tikz[trivalent,every node/.style={basiclabel}]{
        \draw(0,.5)circle(.4)(0,.1)arc(-145:145:.7);
        \node[small matrix]at(-.4,.5){$\mathbf{X}_1$};
        \node[small matrix]at(.4,.5){$\mathbf{X}_2$};
        \node at(-.4,1){$a$};\node at(.5,.95){$b$};\node at(1.2,1.1){$c$};
    }
% rank three
    \tikz[scale=1.4]{
        \draw[trivalent]
            (0,0)to[bend left=80]node[small matrix]{$\xb_1$}(0,1)node[leftlabel,pos=.8]{$a$}
            (0,0)to[bend right=80]node[small matrix]{$\xb_2$}(0,1)node[rightlabel,pos=.8]{$b$}
            (0,0)to[bend right=20](.5,-.2)node[bottomlabel,pos=.5]{$e$}
            to[bend right=80]node[small matrix]{$\xb_3$}(.5,1.2)node[rightlabel,pos=.75]{$c$}
            to[bend right=20](0,1)node[toplabel,pos=.5]{$f$}
            (.5,-.2)to[bend right=20](1,-.4)
            to[bend right=80](1,1.4)node[rightlabel,pos=.75]{$d$}
            to[bend right=20](.5,1.2);
    }
% rank r
    \tikz[scale=1.2]{
        \draw[trivalent]
            (0,0)to[bend left=80]node[small matrix]{$X_1$}(0,1)node[leftlabel,pos=.8]{$d_0$}
            (0,0)to[bend right=80]node[small matrix]{$X_2$}(0,1)node[rightlabel,pos=.8]{$d_1$}
            (0,0)to[bend right=20](.5,-.2)node[bottomlabel,pos=.5]{$f_1$}
            to[bend right=80]node[small matrix]{$X_3$}(.5,1.2)node[rightlabel,pos=.8]{$d_2$}
            to[bend right=20](0,1)node[toplabel,pos=.5]{$e_1$}
            (.5,-.2)to[bend right=20](1,-.4)node[bottomlabel,pos=.5]{$f_2$}
            (1,1.4)to[bend right=20](.5,1.2)node[toplabel,pos=.5]{$e_2$};
        \draw[draw=none](1.25,0)--(2.25,-.2)node[pos=.2]{.}node[pos=.5]{.}node[pos=.8]{.};
        \draw[draw=none](1.25,1)--(2.25,1.2)node[pos=.2]{.}node[pos=.5]{.}node[pos=.8]{.};
        \draw[trivalent,shift={(.5,0)}]
            (1.5,-.6)to[bend right=20](2,-.8)node[bottomlabel,pos=.5]{$f_{r-2}$}
            to[bend right=80]node[small matrix]{$X_r$}(2,1.8)node[leftlabel,pos=.8]{$d_{r-1}$}
            to[bend right=20](1.5,1.6)node[toplabel,pos=.5]{$e_{r-2}$}
            (2,-.8)to[bend right=20](2.5,-1)
            to[bend right=80](2.5,2)node[leftlabel,pos=.8]{$d_r$}
            to[bend right=20](2,1.8);
    }

Other figures for this code:

Other Central Function Forms

\tikz[trivalent]{
        \draw(0,-.3)circle(.4)(0,1.3)circle(.4)(0,.1)to(0,.9);
        \node[basiclabel]at(.5,.1){$a$};\node[basiclabel]at(.5,1.6){$c$};
        \node[rightlabel]at(0,.5){$b$};
        \node[small matrix]at(-.4,-.3){$\bf X$};\node[small matrix]at(-.4,1.3){$\bf Y$};}