In this two-part paper, a MILP sequential synthesis approach based on a new network representation is proposed to facilitate the involvement of the process engineer in the synthesis of series and split heat exchanger networks. The network configuration is defined by choosing the neighboring units for every performed heat match. In this way, the structural conditions specified by the designer to simplify the network complexity can be considered from the beginning by properly restraining the set of feasible neighbors for each potential unit. Such topology constraints usually have a great impact on the problem feasible space, thus preventing from achieving the least utility usage. Consequently, a net heat flow across the pinch normally arises and the notion of pseudo-pinch point becomes worthwhile. The proposed network representation allows to develop a MILP framework to sequentially determine (a) the structural-constrained utility usage target to be achieved by the sought design; (b) the stream pseudo-pinch temperatures and (c) the solution space within which any configuration stands for a network satisfying the design specifications and the constrained utility target. In this way, a realistic network design featuring the lowest number of units can be found and no further modifications to meet the topology conditions will be required. To reduce the size of the MILP network design problem, a decomposition strategy is applied so as to independently find the network configurations at both sides of the stream pseudo-pinch temperatures. Series networks are only considered in Part I. Several examples have successfully been solved in a short C-PU time.