JSFiddle - React, Tailwind, and code Playground

HTML

<div id="display"></div>

JavaScript

var arr = {21: 31, 22: 14, 23: 1, 24: 35, 25: 6, 26: 16, 27: 13, 28: 78, 29: 1,30: 42, 31: 21, 32: 31, 33: 15,34: 20, 35: 24};

var result = {};

Object.entries(arr)
.forEach(item=>{
	if( result[item[1]] == item[0])
  	return;
	if(arr[item[1]] == item[0])
  	result[item[0]] = item[1];
})

document.getElementById("display").innerHTML = `Исходные данные:
${JSON.stringify(arr)}

Результат: 
${JSON.stringify(result)}`;