The social authorization without page reloading is a modern web common problem. Many libraries are resolving backend problems with social auth like Django Social Auth (python/django) or HybridAuth (php/symfony) but no one of them does frontend code. The code below is my simple AngularJS Solution and You can adapt it for any framework even Vanilla.

Code solution

vm.socialAuth = function () {
  var chWindow = $'http://' + $ + '/app/login/vk-oauth2/');
  // in this case /app/login/vk-oauth2/ is a simple django social auth url for
  // replace it by function variable and You will got an multi-network code.
  // $ does open new tab-window
  // without angular is just smth like'/app/login/vk-oauth2/');
  var chInterval = $interval(function() {  // without angular is just setInterval
    if (chWindow.closed) { // chWindow will receive closed state after close
      // the window is closed - we must recheck our session
      $log.debug('child window closed - reload seesion pls =)'); // just console.log
      $interval.cancel(chInterval); // in Vanilla is clearInterval(chInterval);
  }, 100); // do not set to zero! else You can catch some bugs with it.

After that just attach this code to any social auth button like

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Hope that I saved a little bit of your time.