рещение задачи из https://gist.github.com/076a01c53ef1b5701fc2

task.js

function Node(data, left, right) {
    this.data = data;
    this.left = left || null;
    this.right = right || null;
    this.neighbour = null;
}

Node.prototype.toString = function() {
    return "(" + this.data
        + " [" + (this.left || ".") + " " + (this.right || ".") + "]"
        + (this.neighbour ? " -> " + this.neighbour.data : "")
        + ")";
}

function fill_neighbours(root) {
    var cur_layer = [root];
    while(cur_layer.length > 0) {
        var next_layer = [];
        for(var i=0; i < cur_layer.length; i++) {
            var cur_node = cur_layer[i];
            // connect elements of current layer
            if(i>0) {
                cur_layer[i-1].neighbour = cur_node;
            }
            // fill next layer
            cur_node.left && next_layer.push(cur_node.left)
            cur_node.right && next_layer.push(cur_node.right)
        }
        cur_layer = next_layer;
    }
}

var root = new Node(1,
                    new Node(2, new Node(4)),
                    new Node(3, new Node(6), new Node(7)));

console.log("tree before: " + root);
fill_neighbours(root);
console.log("tree after: " + root);