The criterion for drawing an arc between two people is that they have authored some published or forthcoming research together. (For those who have not heard of Erdös numbers, look here.) To lend a bit of parochial interest to the graph, I've coloured my colleagues and other Monash associated people in various ways to help them stand out.
Below you can see a PNG file of the network, but as you can see, it's rather useless. Much better to download the PDF: one-page and four-page versions.
If you know any other philosophers with Erdös numbers, or if you think there are some corrections to be made, please get in touch by email.