Building a tree from a flat array

I am given an array, links:

  const links = [
      {parent: "flare", children: "analytics"} ,
      {parent: "analytics", children: "cluster"} ,
      {parent: "flare", children: "scale"} ,
      {parent: "analytics", children: "graph"} ,
  ];

I want to make it into tree, like so:

const tree = {
 "name": "flare",
 "children": [
  {
   "name": "analytics",
   "children": [
    {
     "name": "cluster",
    },
    {
     "name": "graph",
    }
   ]
  }
 ]
};

Here is my attempt:

function buildTree(links) {

    const map = { }

    const findNodeInChildren = (name, obj) => {
      if (obj[name]) {
        return obj
      } else if (!obj.children) {
        return null
      }

      for (let i = 0; i < obj.children.length; i++) {
        const found = findNodeInChildren(name, obj.children[i])
        if (found) return found
      }

      return null
    }
    
    links.forEach(link => {
      const foundNode = findNodeInChildren(link.parent, map)
      
      if (!foundNode) {
        const newNode = {
          name: link.parent,
          children: []
        }
        map[newNode.name] = newNode
      } else {
          foundNode[link.parent].children.push({
          name: link.children,
          children: []
        })
      }
    })

   return map
}

  const links = [
      {parent: "flare", children: "analytics"} ,
      {parent: "analytics", children: "cluster"} ,
      {parent: "flare", children: "scale"} ,
      {parent: "analytics", children: "graph"} ,
  ];  
  
  const tree = buildTree(links)
  const json = JSON.stringify(tree)
  console.log(json)

Here’s the prettified JSON – it’s not working as intended:

{
  "flare": {
    "name": "flare",
    "children": [
      {
        "name": "scale",
        "children": []
      }
    ]
  },
  "analytics": {
    "name": "analytics",
    "children": [
      {
        "name": "graph",
        "children": []
      }
    ]
  }
}

What is going wrong?