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Multivariate networks are data sets that describe not only the relationships between a set of entities but also their attributes. In this paper, we present a new technique to determine the layout of a multivariate network using Geodesic Self-Organizing Map (GeoSOM). During the training process of a GeoSOM, graph distances are nonlinearly combined with attribute similarities based on the network's graph distance distribution. The resulted layout has less edge crossings than those generated by the previous methods [18]. We conducted a user study to evaluate the effectiveness of this hybrid approach. The results were compared against the most commonly used glyph-based technique. The user study shows that the hybrid approach helps users draw conclusions from both the relationship and vertex attributes of a multivariate network more quickly and accurately. In addition, users found it easier to compare different relationships of the same set of entities. Finally, the capability of the hybrid approach is demonstrated using the world military expenditures and weapon transfer networks.