The Oxford Advanced Learner’s dictionary has an appendix called “Defining Vocabulary”. It says:

“In order to make the dictionary definitions easy to understand, we have written them using only the words in the following list.

[…]

Occasionally it has been necessary to use in a definition a word not in the list. When such a word occurs it is shown in SMALL CAPITAL LETTERS.”

I estimate that list has about 3,500 words.

⇒ If you base your network on that dictionary or one carefully constructed like that, the graph could have a central core of about 3,500 nodes with the other words circling around it.

Making a good visualization still would be a challenge, of course.

(the link is broken though, it should be https://github.com/globalwordnet/english-wordnet)