[Tex/LaTex] How to change the color scheme to make this figure more elegant

Question

Here different colors means different weight of the edge, and the color of the points is arbitrary. The tex code:

  \documentclass[aps,prl,superscriptaddress]{revtex4}
  \usepackage{subfigure}
  \usepackage{tikz}
  \usepackage{pgfplots}
  \usetikzlibrary{shapes.geometric, calc}
  \usepackage[standard]{ntheorem}
  \def\endproof{\vrule height6pt width6pt depth0pt}
  \usepackage{color}
  %%%%%%%%%%%%%%%%%%The color scheme begins
  \definecolor{dsblue}{RGB}{65,105,225}
  \definecolor{spgreen}{RGB}{46,139,87}
  \definecolor{tored}{RGB}{220,20,60}
  \definecolor{glyellow}{RGB}{218,165,32}
  \definecolor{botcolor}{RGB}{119,136,153}
  \definecolor{linecolor}{RGB}{128,128,128}
  \definecolor{topcolor}{RGB}{0,0,139}
  \tikzstyle{mypoint}=[shape=circle,draw,white,bottom color=botcolor,top color= topcolor]
  \tikzstyle{myline}=[linecolor,thin]
  \tikzstyle{mythick}=[thick]
  %%%%%%%%%%%%%%%%%%The color scheme ends
  \begin{document}
  \begin{tikzpicture}[inner sep=0.55mm,scale=0.6]
  \node at (0,1) [mypoint] (a10) {};
  \node at (0,2) [mypoint] (a11) {};
  \node at (0,3) [mypoint] (a12) {};
  \node at (0,4) [mypoint] (a13) {};
  \node at (0,5) [mypoint] (a14) {};
  \node at (0,-1) [mypoint] (a20) {};
  \node at (0,-2) [mypoint] (a21) {};
  \node at (0,-3) [mypoint] (a22) {};
  \node at (0,-4) [mypoint] (a23) {};
  \node at (0,-5) [mypoint] (a24) {};
  \node at (1,0) [mypoint] (b10) {};
  \node at (2,0) [mypoint] (b11) {};
  \node at (3,0) [mypoint] (b12) {};
  \node at (4,0) [mypoint] (b13) {};
  \node at (5,0) [mypoint] (b14) {};
  \node at (-1,0) [mypoint] (b20) {};
  \node at (-2,0) [mypoint] (b21) {};
  \node at (-3,0) [mypoint] (b22) {};
  \node at (-4,0) [mypoint] (b23) {};
  \node at (-5,0) [mypoint] (b24) {};
  %%%%%%%%%%%a1-b1=0=a2-b2=b2-a1,a2-b1=0,b1-a2-1=-1=4,4-4=0
  \foreach \n/\m in {0/0,1/1,2/2,3/3,4/4} {
 \draw [glyellow,mythick] (a1\n) -- (b1\m);
 \draw [glyellow,mythick] (a2\n) -- (b2\m);
 \draw [glyellow,mythick] (b2\n) -- (a1\m);
  }
  %%%%%%%%%%%a1-b1=-1=4=a2-b2=b2-a1,a2-b1=-1,b1-a2-1=0,4-0=4
  \foreach \n/\m in {0/1,1/2,2/3,3/0} {
  \draw [glyellow,mythick] (a2\n) -- (b1\m);
  }
  %%%%%%%%%%%a1-b1=1=a2-b2=b2-a1,a2-b1=1,b1-a2-1=-2=3,4-3=1
  \foreach \n/\m in {1/0,2/1,3/2,4/3,0/4} {
  \draw [spgreen,mythick] (a2\n) -- (b1\m);
  \draw [tored,mythick] (a1\n) -- (b1\m);
  \draw [tored,mythick] (a2\n) -- (b2\m);
  \draw [tored,mythick] (b2\n) -- (a1\m);
  }
  %%%%%%%%%%%a1-b1=2=a2-b2=b2-a1,a2-b1=2,b1-a2-1=-3=2,4-2=2
  \foreach \n/\m in {2/0,3/1,4/2,0/3} {
  \draw [dsblue,mythick] (a2\n) -- (b1\m);
  \draw [dsblue,mythick] (a1\n) -- (b1\m);
  \draw [dsblue,mythick] (a2\n) -- (b2\m);
  \draw [dsblue,mythick] (b2\n) -- (a1\m);
  }
  %%%%%%%%%%%a1-b1=3=a2-b2=b2-a1,a2-b1=3,b1-a2-1=-4=1,4-1=3
  \foreach \n/\m in {3/0,4/1,0/2,1/3} {
  \draw [tored,mythick] (a2\n) -- (b1\m);
  \draw [spgreen,mythick] (a1\n) -- (b1\m);
  \draw [spgreen,mythick] (a2\n) -- (b2\m);
  \draw [spgreen,mythick] (b2\n) -- (a1\m);
  }
  \foreach \n/\m in {0/1,1/2,2/3,3/4} {
  \draw [linecolor,thin] (a1\n) -- (a1\m);
  \draw [linecolor,thin] (a2\n) -- (a2\m);
  \draw [linecolor,thin] (b1\n) -- (b1\m);
  \draw [linecolor,thin] (b2\n) -- (b2\m);
  }
  \node [above] at (a14) {$A_1$};
  \node [below] at (a24) {$A_2$};
  \node [right] at (b14) {$B_1$};
  \node [left] at (b24) {$B_2$};
  \end{tikzpicture}
  \end{document}

Answer 1

Concerning the answers of the OP i tried som thing like encoding the value into line thickness, which didn't look so nice. Instead, the following does encode the value in monochromatic values (using light and dark blue) i renamed the colornames to semantics (v1,..., v4 and v5 which i think (linecolor might be - no value?) and set their colors.

I adapted the for loops for the \nodes and increased the label distance a little bit, but the rest of the code is unchanged

\documentclass[aps,prl,superscriptaddress]{revtex4}
    \usepackage{subfigure}
    \usepackage{tikz}
    \usepackage{pgfplots}
    \usetikzlibrary{shapes.geometric, calc}
    \usepackage[standard]{ntheorem}
    \def\endproof{\vrule height6pt width6pt depth0pt}
    \usepackage{color}
    %%%%%%%%%%%%%%%%%%The color scheme begins
    \tikzset{% was glyellow
    v1/.style={line width=.5pt,blue!33!black},
% was spgreen
    v2/.style={line width=.5pt,blue!66!black},
% was tored
    v3/.style={line width=.5pt,blue!33},
%was dsblue
    v4/.style={line width=.5pt,blue!66},
% was linecolor (no value?)
    v5/.style={line width=.5pt,black}
    }
    \tikzstyle{mypoint}=[shape=circle,draw,white,fill=black,label distance=2ex]
    \begin{document}
    \begin{tikzpicture}[inner sep=0.55mm,scale=0.6]
    \foreach \a in {0,...,4} \node at (0,\a+1) [mypoint] (a1\a) {};
    \foreach \a in {0,...,4} \node at (0,-\a-1) [mypoint] (a2\a) {};
    \foreach \b in {0,...,4} \node at (\b+1,0) [mypoint] (b1\b) {};
    \foreach \b in {0,...,4} \node at (-\b-1,0) [mypoint] (b2\b) {};
    %%%%%%%%%%%a1-b1=0=a2-b2=b2-a1,a2-b1=0,b1-a2-1=-1=4,4-4=0
    \foreach \n/\m in {0/0,1/1,2/2,3/3,4/4} {
 \draw [v1] (a1\n) -- (b1\m);
 \draw [v1] (a2\n) -- (b2\m);
 \draw [v1] (b2\n) -- (a1\m);
    }
    %%%%%%%%%%%a1-b1=-1=4=a2-b2=b2-a1,a2-b1=-1,b1-a2-1=0,4-0=4
    \foreach \n/\m in {0/1,1/2,2/3,3/0} {
    \draw [v1] (a2\n) -- (b1\m);
    }
    %%%%%%%%%%%a1-b1=1=a2-b2=b2-a1,a2-b1=1,b1-a2-1=-2=3,4-3=1
    \foreach \n/\m in {1/0,2/1,3/2,4/3,0/4} {
    \draw [v2] (a2\n) -- (b1\m);
    \draw [v3] (a1\n) -- (b1\m);
    \draw [v3] (a2\n) -- (b2\m);
    \draw [v3] (b2\n) -- (a1\m);
    }
    %%%%%%%%%%%a1-b1=2=a2-b2=b2-a1,a2-b1=2,b1-a2-1=-3=2,4-2=2
    \foreach \n/\m in {2/0,3/1,4/2,0/3} {
    \draw [v4] (a2\n) -- (b1\m);
    \draw [v4] (a1\n) -- (b1\m);
    \draw [v4] (a2\n) -- (b2\m);
    \draw [v4] (b2\n) -- (a1\m);
    }
    %%%%%%%%%%%a1-b1=3=a2-b2=b2-a1,a2-b1=3,b1-a2-1=-4=1,4-1=3
    \foreach \n/\m in {3/0,4/1,0/2,1/3} {
    \draw [v3] (a2\n) -- (b1\m);
    \draw [v2] (a1\n) -- (b1\m);
    \draw [v2] (a2\n) -- (b2\m);
    \draw [v2] (b2\n) -- (a1\m);
    }
    \foreach \n/\m in {0/1,1/2,2/3,3/4} {
    \draw [v5] (a1\n) -- (a1\m);
    \draw [v5] (a2\n) -- (a2\m);
    \draw [v5] (b1\n) -- (b1\m);
    \draw [v5] (b2\n) -- (b2\m);
    }
    \node [above=1ex] at (a14) {$A_1$};
    \node [below=1ex] at (a24) {$A_2$};
    \node [right=1ex] at (b14) {$B_1$};
    \node [left=1ex] at (b24) {$B_2$};
    \end{tikzpicture}
\end{document}

If one of the values is of special interest, one could also adapt the colors to represent 3 values (blue!50!black, blue and blue!50!white and a highlight color). The image for the monocromatic approach looks like the following, which I think is easier to catch