Netlify doesn't run a app server like Heroku, it only runs a static file server. From your code, it appears that you're trying to serve a app that you could connect to and provide yourself with GraphQL access. This is not possible on Netlify, at least not directly.
The only server-like solution that Netlify currently provides in Netlify Functions. However, those are limited to 10 sec by default and provide, one-time data connection - not something that you could keep on using for GraphQL.
So if your requirement is to keep the GraphQL server running (for example like what Gatsby does during gatsby develop
), Netlify is not the solution for you. If you wish to send the data one-time and add some server-side processing, you can take a look at Netlify Functions.