There were several solutions around, but none of them did what I really wanted: take some nice, working D3js graph visualisation code and feed it with .dot file instead of .json file.
That's why I created an adapter which will basically allow you to use .dot files with any of thousands of D3js samples by changing just one statement. If you have some D3js visualisation working on following data-structure:
{
  "nodes": [ {"id": "Myriel"}, {"id": "Napoleon"}],
  "links": [ {"source": "Myriel"}, {"target": "Napoleon"}]
} 
Just include following script and call d3.dot:
<script src="https://cdn.jsdelivr.net/gh/gmamaladze/d3-dot-graph@1.0.0/build/d3-dot-graph.min.js"></script>
<script>
d3.dot(url, function(graph) {
   ...
});
</script>
instead of:
d3.json(url, function(graph) {...});
GitHub repository with code and examples