Visual C++ :: Creating Matrix / Map For Topological Sort?

I am trying to simulate the logical circuits having NAND gates. I am reading the structure from .bench file. The structure of a circuit looks like below:

Code:
INPUT(1)
INPUT(2)
INPUT(3)
INPUT(6)
INPUT(7)
10 = NAND(1, 3)
11 = NAND(3, 6)
16 = NAND(2, 11)
19 = NAND(11, 7)
22 = NAND(10, 16)
23 = NAND(16, 19)

It can be seen that the inputs for Gate 22 are 10 and 16 which are also NAND gates. On the other hand, for gate 10, the inputs are 1 and 3 which are simple inputs. So, i need to sort the gates topologically. Although topological sort will not affect the output for this particular example but i have big circuits also in which topological sort is required. But we can use this simple example to do the topological sort.

My effort:I thought to create a map which will keep the information about the gate name and its indegree. But i am unable to proceed further.

Code:
void Circuit::topologicalSort()//topological sorting (for the mixed circuits) {
int counter = 0;
std::map<string, int> unsortTopoList; //this list keeps a track of gate name and its Indegree
for(int i=0; i<gates.size(); i++) {

[code].....