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I want to make Star topology graph, which have the source and the target node from a json file

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You could try visjs. I like it because R has a nice package for visjs binding, but visjs' maintenance status is unclear to me.

More requirements please: should it be interactive, mutable with the mouse, or have nice text labels, etc?

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By far the most popular JS data visualization library is D3Js (and it's free :-)

Take a look at the gallery.

The S.O question "D3 How do I create a Star Layout for a force directed map?" ought to interest you, and shows how to draw this:

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