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I need to draw a binomial tree, where nodes with the same value are merged together. Example: Text (But instead from left to right, I want it to be from up to down). Is there a way to do this with tikz-qtree? I am very new to tikz, so I would like to avoid any complex solutions. But also, it is necessary that i can label the edges (and if possible, draw arrows instead of undirected edges).

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If you want something simple I would recommend you tikz with automata library. The following code is very self-explanatory (or so I think):

\documentclass[border=2mm]{standalone}
\usepackage    {tikz}
\usetikzlibrary{automata}
\begin{document}
\begin{tikzpicture}[->,-latex,shorten >=1pt,auto,node distance=25mm,semithick]
\node[state](1)                  {$100$};
\node[state](2)[below left  of=1] {$95$};
\node[state](3)[below right of=1]{$105$};
\node[state](4)[below left  of=2] {$90$};
\node[state](5)[below right of=2]{$100$};
\node[state](6)[below right of=3]{$110$};
\path (1) edge [swap] node {a}(2)
      (1) edge        node {b}(3)
      (2) edge [swap] node {c}(4)
      (2) edge        node {d}(5)
      (3) edge [swap] node {e}(5)
      (3) edge        node {f}(6);
\end{tikzpicture}
\end{document}

And draws this tree: enter image description here

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