The concept of fairness index for self-authority servers in a large-scale network is introduced in this paper. The index quantifies the relative contributions of the servers to network routing, and can be used in network administration processes, such as negotiation of Multi-Lateral Peering Agreements. The fairness index concept leads naturally to the idea of an absolutely fair solution, which is a study focus in this paper. Although, an absolutely fair solution may not be an ideal operating point due to efficiency considerations, it serves as a reference point for comparing contribution from various servers in a network. Uniqueness and existence properties of absolutely fair solutions are examined in general as well as for certain specially structured networks of interest. Via the concept of a pricing duality, the connection of absolutely fair solutions to the von Neumann economic model is established. For implementation considerations, a distributed, low-data-rate control algorithm that converges to pre-defined fairness index targets is introduced and analyzed. A heuristic extension is studied to provide a practical approach for realistic situations.