Different researchers have comprehensively addressed the water distribution network (WDN) optimization design problem in the past years. However, in the analysis of the optimized WDN, the relationship between the geometric parameters of the network and the hydraulic parameters obtained from the optimal design has been set aside. In this research, a robust geometric analysis of optimal WDN designs by pipe cost minimization is made in order to provide a response to the possible relationships between the geometry of the network and its optimized design. In addition, geometrical analysis is performed understanding that water distribution infrastructure, represented as a spatially organized graph, is a complex network of interconnected vertices (nodes) and edges (pipes) that belong to the emerging topic of complex network theory (CNT). Therefore, CNT metrics along with other geometric aspects (e.g., pipe diameter, pipe length, fractality, branch index, among others) of the network are measured for analyzing features of the physical domain where hydraulics and optimization occurs. As a result, it was determined how the effectiveness and efficiency of optimization methodologies are affected depending on the network topology.