UPDATE: the other possible solution (with D3.js) is using so called hierarchical edge layout yet the links between nodes might not be simple arcs e.g. they are more variations in curves/links.
Hi there, I'm Matt Sergei (do call me Matt, please) and can help you -
what you need (based on your provided URL reference chart) is a D3.js force layout (that will automatically draw links between nodes, some scripting is required for curved links) and with "fixed" nodes position (scripting is required for that too, possibly circular force could be used but it places nodes only in a circle, not ellipsis as in your case).
It can be done though - I can do it today (just provide me a dataset e.g. a list of nodes and a list of links - if you have explored [login to view URL]@d3/force-directed-graph?collection=@d3/d3-force example, you can see what format the variable "data" needs to be e.g. a JSON file).
Otherwise I'm a webmaster and developer for 26 years, probably top D3.js developer here (usually fixing incomplete work by other freelancers, 4 times last year).
Regards and hope you're safe,
Matt