How to get, resolve and verify transitive/cyclic dependency

var v1 = 'asd';
var v2 = '@@{v1}@@';
var v3 = '@@{v2}@@';
var v4 = '@@{v3}@@';
var v5 = '@@{v4}@@';
var v6 = '@@{v5}@@_@@{v3}@@';

var a1 = '@@{v1}@@_@@{a3}@@';
var a2 = '@@{a1}@@';
var a3 = '@@{a2}@@';

var x1 = 'asd';
var x2 = '@@{x1}@@';
var x3 = '@@{x1}@@_@@{x2}@@';

var p1 = '@@{v4}@@_@@{xyz}@@';
var p2 = '@@{xyz}@@';

const getVariableNames = str => {
    str += '';
    const variables = str.match(/(@@{[^}{)(\]\[\-+*\/]+?}@@)+?/g);
    return variables && variables.length ? variables.map(i => i.substring(3, i.length - 3)) : false;
};

const isCyclic = (myMap, node, target, [...visited] = []) => {
    if (myMap[node]) {
        if (node === target) {
            return true;
        }
        if (visited.includes(node) || !myMap[node].dep.usedIns) {
            return false;
        }
        visited.push(node);
        return myMap[node].dep.usedIns.some(n => isCyclic(myMap, n, target, visited));
    }
};

var allVars = [{ name: 'v1', val: v1 }, { name: 'v2', val: v2 },
    { name: 'v3', val: v3 }, { name: 'v4', val: v4 }, { name: 'v5', val: v5 }, { name: 'v6', val: v6 },
    { name: 'a1', val: a1 }, { name: 'a2', val: a2 }, { name: 'a3', val: a3 }, { name: 'x1', val: x1 },
    { name: 'x2', val: x2 }, { name: 'x3', val: x3 }];

function getValueMap(arr) {
    // need to get implemented
    var nodeAVL = [];
    const varNamesMap = arr.reduce((a, b) => {
        a[b.name] = { ...b, v: getVariableNames(b.val), dependsOn: [], usedIn: [], cyclic: [], unresolved: [] };
        return a;
    }, {});
    return varNamesMap;
}

var retVar = getValueMap(allVars);

console.log(retVar);
// should console
/* {
    v1: { val: 'asd', dependsOn: [], usedIn: ['v2', 'v3', 'v4', 'v5', 'v6', 'p1'], cyclic: [], unresolved: [] },
    v2: { val: 'asd', dependsOn: ['v1'], usedIn: ['v3', 'v4', 'v5', 'v6'], cyclic: [], unresolved: [] },
    v3: { val: 'asd', dependsOn: ['v2'], usedIn: ['v4', 'v5', 'v6'], cyclic: [], unresolved: [] },
    v4: { val: 'asd', dependsOn: ['v3'], usedIn: ['v5', 'v6'], cyclic: [], unresolved: [] },
    v5: { val: 'asd', dependsOn: ['v4'], usedIn: ['v6'], cyclic: [], unresolved: [] },
    v6: { val: 'asd_asd', dependsOn: ['v5', 'v3'], usedIn: [], cyclic: [], unresolved: [] },

    a1: { val: '', dependsOn: ['v1'], usedIn: [], cyclic: ['a1', 'a2', 'a3'], unresolved: [] },
    a2: { val: '', dependsOn: [], usedIn: [], cyclic: ['a1', 'a2', 'a3'], unresolved: [] },
    a3: { val: '', dependsOn: [], usedIn: [], cyclic: ['a1', 'a2', 'a3'], unresolved: [] },

    x1: { val: 'asd', dependsOn: [], usedIn: [], cyclic: [], unresolved: [] },
    x2: { val: 'asd', dependsOn: ['x1'], usedIn: ['x3'], cyclic: [], unresolved: [] },
    x3: { val: 'asd_asd', dependsOn: ['x1', 'x2'], usedIn: [], cyclic: [], unresolved: [] },

    p1: { val: '', dependsOn: ['v4'], usedIn: [], cyclic: [], unresolved: ['xyz'] },
    p2: { val: '', dependsOn: [], usedIn: [], cyclic: [], unresolved: ['xyz'] },
};*/