BreadthFirstSearch.js

/**
 *       10
 *      /  \
 *     4    17
 *    / \   / \
 *   1   9 12  18
 *  /
 * 22
 */

const graphList = [
  [10, 4, 17],
  [4, 1, 9],
  [17, 12, 18],
  [1, 22],
  [9],
  [12],
  [18],
  [22],
];

const graph = new Map();

function addNodes(node, left = null, right = null) {
  graph.set(node, { value: node, left, right });
}

graphList.forEach(nodes => addNodes(...nodes));

function BreadthFirstSearch(graph, root, value) {
  const path = [];
  const queue = [graph.get(root)];

  while (queue.length > 0) {
    const currentNode = queue.shift();
    path.push(currentNode.value);

    if (currentNode.value === value) {
      return path;
    }

    if (currentNode.left) {
      queue.push(graph.get(currentNode.left));
    }

    if (currentNode.right) {
      queue.push(graph.get(currentNode.right));
    }
  }

  console.log('Could not find the node');
  return [];
}

console.log('graph:', graph);
console.log(BreadthFirstSearch(graph, 10, 12));
console.log(BreadthFirstSearch(graph, 17, 18));
console.log(BreadthFirstSearch(graph, 10, 22));
console.log(BreadthFirstSearch(graph, 10, 99));

Output from the console.logs():

graph: Map(8) {
  10 => { value: 10, left: 4, right: 17 },
  4 => { value: 4, left: 1, right: 9 },
  17 => { value: 17, left: 12, right: 18 },
  1 => { value: 1, left: 22, right: null },
  9 => { value: 9, left: null, right: null },
  12 => { value: 12, left: null, right: null },
  18 => { value: 18, left: null, right: null },
  22 => { value: 22, left: null, right: null }
}
[ 10, 4, 17, 1, 9, 12 ]
[ 17, 12, 18 ]
[ 10,  4, 17,  1, 9, 12, 18, 22 ]
Could not find the node
[]