Create separate double arrows as edge of a tree

Question

I'd like to create a tree with edges made from two separate arrows as shown in picture:

But I don't know how to change the edge to 'two separate arrows for each edge' Currently, I could only do the diagram below:

Below is the sample code:

\documentclass{article}

\usepackage[latin1]{inputenc}
\usepackage{tikz}
\usetikzlibrary{trees}
\begin{document}
\pagestyle{empty}


\tikzstyle{level 1}=[level distance=3.5cm, sibling distance=3.5cm]
\tikzstyle{level 2}=[level distance=3.5cm, sibling distance=2cm]
\tikzstyle{bag} = [text width=4em, text centered]

\begin{tikzpicture}[sloped]
\node[bag] {1}
    child {
        node[bag] (2) {2}        
            child {
                node (4) {4}
                edge from parent [<->, thick]
                node[above] {e}
                node[below]  {f}
            }
            child {
                node (5) {5}
                edge from parent [<->, thick]
                node[above] {g}
                node[below]  {h}
            }
            edge from parent [<->, thick]
            node[above] {a}
            node[below]  {b}
    }
    child {
        node[bag] (3) {3}        
        child {
                node (6) {6}
                edge from parent [<->, thick]
                node[above] {i}
                node[below]  {j}
            }
            child {
                node (7) {7}
                edge from parent [<->, thick]
                node[above] {k}
                node[below]  {l}
            }
        edge from parent [<->, thick]          
            node[above] {c}
            node[below]  {d}
    };

\path (2) -- (3) node [midway] {$\cdots$};
\path (4) -- (5) node [midway] {$\cdots$};
\path (6) -- (7) node [midway] {$\cdots$};

\end{tikzpicture}

\end{document}

Appreciate any help. Thanks!

Answer 1

Welcome to TeX.SE! Luckily this has been worked out in this great undervoted answer, which I just apply.

\documentclass{article}

\usepackage[latin1]{inputenc}
\usepackage{tikz}
\usetikzlibrary{trees,arrows.meta}
\makeatletter

\pgfkeys{
  /pgf/arrow keys/.cd,
  Bidirectional/.style={
    length = +1.05pt 1.925 1,
    shear
  },
  shear/.code={
    \pgfarrowsthreeparameters{#1}%
    \expandafter\pgfarrowsaddtooptions\expandafter{\expandafter\pgfarrowslinewidthdependentnew\pgfarrowstheparameters\pgfarrowshear\pgf@x}%
  },
  shear/.default = +0pt -.5 -.5
}
\newdimen\pgfarrowshear
\pgfarrowshear0pt
\def\pgfarrowslinewidthdependentnew#1#2#3{%
  \pgf@x#1%
  \ifdim\pgfinnerlinewidth>0pt%
    \pgf@arrows@inner@line@width@depnew{#2}{#3}%
  \else%  
    \advance\pgf@x by#2\pgflinewidth%
  \fi%
}
\def\pgf@arrows@inner@line@width@depnew#1#2{%
  % #1 * outer line width + #2 * inner line width = our new one = the following
  % (#1/2) * full line width + (#2-#1/2) * inner line width)
  % Compute "real" line width
  \pgf@xa.5\pgflinewidth%
  \pgf@xa#1\pgf@xa%
  \advance\pgf@x by\pgf@xa%
  \pgf@xa\pgfinnerlinewidth%
  \pgf@xb.5\pgf@xa%
  \advance\pgf@x by#2\pgf@xa%
  \advance\pgf@x by-#1\pgf@xb%
}
\def\pgf@arrow@drawer@shift#1#2#3{
  \pgftransformyshift\pgfarrowshear%
  \pgf@xb#2\pgftransformxshift{-\pgf@xb}%
  \pgf@xc#1%
  \advance\pgf@xc by\pgfarrowsep%
  \advance\pgf@xc by-\pgf@xb%
}
\makeatother
\begin{document}
\pagestyle{empty}


\begin{tikzpicture}[sloped,
level 1/.style={level distance=3.5cm, sibling distance=3.5cm},
level 2/.style={level distance=3.5cm, sibling distance=2cm},
bag/.style={text width=4em, text centered},
bidi/.style={thick,double,double
distance=3pt,{<[Bidirectional]}-{>[Bidirectional]}}]
\node[bag] {1}
    child {
        node[bag] (2) {2}        
            child {
                node (4) {4}
                edge from parent [bidi]
                node[above] {e}
                node[below]  {f}
            }
            child {
                node (5) {5}
                edge from parent [bidi]
                node[above] {g}
                node[below]  {h}
            }
            edge from parent [bidi]
            node[above] {a}
            node[below]  {b}
    }
    child {
        node[bag] (3) {3}        
        child {
                node (6) {6}
                edge from parent [bidi]
                node[above] {i}
                node[below]  {j}
            }
            child {
                node (7) {7}
                edge from parent [bidi]
                node[above] {k}
                node[below]  {l}
            }
        edge from parent [bidi]          
            node[above] {c}
            node[below]  {d}
    };

\path (2) -- (3) node [midway] {$\cdots$};
\path (4) -- (5) node [midway] {$\cdots$};
\path (6) -- (7) node [midway] {$\cdots$};

\end{tikzpicture}

\end{document}