Rural areas in the developing countries are predominantly devoid of Internet access as it is not viable for operators to provide broadband service in these areas. To solve this problem, we propose a middle mile Long erm Evolution Advanced (LTE-A) network operating in TV white space to connect villages to an optical Point of Presence (PoP) located in the vicinity of a rural area. We study the problem of spectrum sharing for the middle mile networks deployed by multiple operators. A graph theory based Fairness Constrained Channel Allocation (FCCA) algorithm is proposed, employing Carrier Aggregation (CA) and Listen Before Talk (LBT) features of LTE-A. We perform extensive system level simulations to demonstrate that FCCA not only increases spectral efficiency but also improves system fairness.