In the field of global history, especially when it comes to « histoire croisée », the use of metaphors describing the vertical organization of a society, its structuration into layers or into overlapping systems, is common. The temptation to use a second metaphor, calling everything a “network”, is also very important in this domain, whose objects of study are often transnational organizations with multiple branches, intertwined within umbrella organizations, sharing board members and including several levels of secretariats and subcommittees (Grandjean 2017). However, the use of these images is not limited to historical studies, since we use the same vocabulary in other disciplines to describe social situations or textual structures. When we go beyond the metaphor to develop a formal analysis, we often produce multigraphs who, because they simultaneously express horizontal and vertical relationships, are generally unsuitable for the analysis (and visualisation, except in very simple cases). If the “exploratory” dimension of social network analysis – and especially the fact that its display is relatively subjective – is often a subject of criticism, we propose here to play with the visual representation to show precisely how an original modelling can improve the reading of complex graphs, and helping to restore a “morphological” (Moretti 1999, 68) information where disorder seems to prevail. Based on two examples from archives mapping and theatre character networks, this paper proposes a reflection on the different ways to take account of verticality in graphs. In particular, we are developing a way to impose a macro-structure to a network, allowing a two-dimensions view that reflects the hierarchical affiliations of its components. We will see that this method, by constructing a stable visual representation in time and space, helps to compare different types of relationships and/or different time states of the graph.