In the following code, the head and tail labels overlap the arrow, which I do not want. What do I have to do?
digraph G {
    node [shape = "record"];
    edge [
      arrowhead = "normal"
      headlabel = "0..*"
      taillabel = "longlabel"
    ];
    N1 [ label="N1"];         
    N2 [label = "N2" ];       
    N1->N2;
}
You can't really control the position of head and tail-labels as it is possible for the edge label (using labelangle, labeldistance, etc.)
However, as a hack, you could add whitespace to the head/tail-label and that way force the center of the label to be on the left or right of the label text:
  headlabel = "        0..*"
  taillabel = "longlabel             "
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