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is there a way to make an edge (E) like this with tikz package. I know I can bend them to some degree, but I would like to make them as big as I require. Thank you for any help.

enter image description here

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    Your question leaves all the effort to our community, even typing the essentials of a TeX document such as \documentclass \begin{document} etc. As it is, most of our users will be very reluctant to touch your question, and you are left to the mercy of our procrastination team who are very few in number and very picky about selecting questions. You can improve your question by adding a minimal working example (MWE) that more users can copy/paste onto their systems to work on. If no hero takes the challenge we might have to close your question. (meta.tex.stackexchange.com/questions/4267) – Dr. Manuel Kuehner Mar 7 '16 at 20:10
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You can use the controls syntax to draw bezier curves. In the example below I used relative coordinates as that was convenient. The important to note is that the first control point will be relative to the previous coordinate in the path (here a), while the second control point is relative to the next coordinate in the path (here b).

enter image description here

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}
\node [draw,circle] (a) {};
\node [draw,circle] (b) at (3,0) {};

\draw (a) .. controls +(0,1) and +(0,1) .. (b) node[midway,above] {E};
\draw [red] (a) .. controls +(0,3) and +(0,3) .. (b) node[midway,above] {E};
\draw [blue] (a) .. controls +(-2,4) and +(2,4) .. (b) node[midway,above] {E};
\end{tikzpicture}
\end{document}

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