Simple minimum spanning tree (MST) implementation in JS; note: the cycle checking function works for this small graph, but will need to be implemented in larger graphs

MST.js

const vertices = ['a', 'b', 'c', 'd'];
const edges = [
  {
    starting: 'c',
    ending: 'd',
    weight: 500,
  },
  {
    starting: 'a',
    ending: 'b',
    weight: 1,
  },
  {
    starting: 'b',
    ending: 'c',
    weight: 1,
  },
  {
    starting: 'c',
    ending: 'd',
    weight: 1,
  }
];  

// Note: I didn't actually implement the cycle checking algorithm,
//       but functionally it's the same for the given graph G.
const doesGraphContainAtleastOneCycle = (arr) => {
  return false;
};

const findMinimumSpanningTree = () => {
  // O(E log E)
  let sortedEdges = edges.sort((a, b) => {
    if (a.weight < b.weight) return -1;
    else if (a.weight > b.weight) return 1;
    else return 0;
  });

  const minimumSpanningTree = [];
  while (sortedEdges.length > 0 && minimumSpanningTree.length < (vertices.length - 1)) {
    const tempEdge = sortedEdges.shift();
    
    // If a cycle exists with the new edge, then don't push it into the MST array
    const tempMST = [...minimumSpanningTree, tempEdge];
    if (doesGraphContainAtleastOneCycle(tempMST)) continue;

    minimumSpanningTree.push(tempEdge);
  }

  return minimumSpanningTree.length === (vertices.length - 1)
    ? minimumSpanningTree
    : null;
};

const result = findMinimumSpanningTree();
console.log(result);