Networks are a common way to model systems, organizational systems that design these systems, and systems of systems that receive/benefit from these designed systems. They may contain hundreds or thousands of nodes and edges, which may decrease capacity to understand, analyze and make decisions. This paper tests the possibility to remove some elements in networks, mainly weak edges, in order to know if and how much precision is lost in terms of analysis. The results show that, first it is possible in some situations to make such a simplification, since the simplified network analysis is closer to the complete network analysis than the basic analysis, often made without network consideration. Second, this precision is still sensitive to the structure of the initial network and the position of weak links. Several tests on real past modeled networks are made to illustrate this research.