Converting circular structure to JSON on JSON.stringify / this is a version of the solution for Vue.js

stringify.js

// http://stackoverflow.com/questions/11616630/json-stringify-avoid-typeerror-converting-circular-structure-to-json/11616993#11616993

//this is a version for Vue.js
//filters vue.js internal properties

//you can extend Vue object instead
Object.stringify  = function(value, space) {
    var cache = [];

    var output = JSON.stringify(value, function (key, value) {

        //filters vue.js internal properties
        if(key && key.length>0 && (key.charAt(0)=="$" || key.charAt(0)=="_")) {

            return;
        }

        if (typeof value === 'object' && value !== null) {
            if (cache.indexOf(value) !== -1) {
                // Circular reference found, discard key
                return;
            }
            // Store value in our collection
            cache.push(value);
        }


        return value;
    }, space)

    cache = null; // Enable garbage collection

    return output;
}

//---------------------------------
var o = {};
o.o = o;


var demo = new Vue({
    el: '#el',
    data: {a:1, b:"s"},
    methods: {}
});

console.log( Object.stringify(demo,2));
console.log( Object.stringify(o));
//---------------------------------
//same code, 2nd option --> in prototype

Object.prototype.stringify= function(space) {
        var cache = [];

        var output = JSON.stringify(this, function (key, value) {

            //filters vue.js internal properties
            if(key && key.length>0 && (key.charAt(0)=="$" || key.charAt(0)=="_")) {
                    return;
                }

            if (typeof value === 'object' && value !== null) {
                if (cache.indexOf(value) !== -1) {
                    // Circular reference found, discard key
                    return;
                }
                // Store value in our collection
                cache.push(value);
            }

            return value;
			
        }, space)

        cache = null; // Enable garbage collection

        return output;
    }




//---------------------------------
console.log( demo.stringify());
console.log( o.stringify());
console.log( demo.stringify(2));   //indentation