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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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


\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};

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