The Edge object is used to link Nodes together and its implementation is straightforward.
struct Edge {
  ...
  /// The function this `Edge` points to.
  std::shared_ptr<Node> function;
  /// The identifier of a particular input to the function.
  uint32_t input_nr;
};

It only requires a function pointer (the actual grad_fn objects that the edges link together), and an input number that acts as an id for the edge.
Linking nodes together
When we invoke the product operation of two tensors, we enter into the realm of autogenerated code. All the scripts that we saw in tools/autograd fill a series of templates that wrap the differentiable functions in ATen. These functions have code to construct the backward graph during the forward pass.