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Graph of co-authors from data in the Brede Wiki. Only the authors with a Paul Erdős-number less than 5 are shown. Paul Erdős is in the lower left corner; Karl J. Friston at the top with Erdős-number 4.
Interestingly John J. Sidtis has an Erdős-number on 3 from two independent paths.
I am/was a bit suspicious about Mr. “J. Gilles”. I cannot find much information about him. I got this path from the Erdős–Bacon number article on Wikipedia which leads to Jonathan D. Victor’s page. I suppose Professor Victor knows his coauthors, so there shouldn’t be a problem. J. Gilles is according to Victor “Joseph Gilles”. One Internet page states “During the war Gillis made a significant contribution to code breaking at Bletchley Park” (http://www.jameshamiltonphysicist.com/5-inst-and-queens/). Possibly the same person.