A Majority-Inverter Graph (MIG) is a homogeneous logic network, where each node represents the majority function. Recently, a logic optimization package based on the MIG data-structure, with 3-input majority node (M3) has been proposed [2], [30]. It is demonstrated to have efficient area-delay-power results compared to state-of-the-art logic optimization packages. In this paper, the Boolean algebraic transformations based on majority logic, i.e., majority Boolean algebra is studied. In the first part of this paper, we summarize a range of identities for majority Boolean algebra with their corresponding proofs. In the second part, we venture towards heterogeneous logic network and provide reversible logic mapping of majority nodes.