A function will traverse a tree passed as an argument. The function will add the number values contained on each node when available.

traverse-and-add.js

// Will traverse a tree passed as an argument. The function will add the number values contained on each node when available.
function traverseAndAdd(tree) {

        // Init var to contain sum of values
        var sum = 0;

        // Function will traverse nodes
        var recursiveCrawl = function (branch) {

                for (i in branch) {

                        // If node contains children use recursion to reach children
                        if ( typeof branch[i] == "object" ) {
                                recursiveCrawl (branch[i]);
                        }

                        // Child node has no children, if is a number, add it to the total sum
                        else if (typeof branch[i] == "number"){

                                // Add value to total sum
                                sum = sum + branch[i];
                        }
                }
        }

        // Call function
        recursiveCrawl(tree);

        // Return total sum of nodes' values
        return sum;
}

tree-for-testing.js

//  Use to test function. JSON object, tree structure.
var tree = {
    "id": 100,
    "children": [
        {
            "id": 110,
            "children": [
                {
                    "id": 111
                },
                {
                    "id": 112
                }
            ]
        },
        {
            "id": 120,
            "children": [
                {
                    "id": 121
                },
                {
                    "id": 122
                }
            ]
        },
        {
            "id": 130,
            "children": [
                {
                    "id": 131
                },
                {
                    "id": 132
                }
            ]
        }
    ]
}