If you want to get the citation network from the table with the DOI, you can use Table2Net in "citation" mode :)
See also our other tools at Médialab Tools!
BiblioTools was developed by Sebastian Grauwin for a similar purpose. It is dedicated to getting networks from Web of Science, and can deal a large mass of data.
We recommand to use Gephi for spatializing networks. It is more efficient than this website. Check its tutorials!