Multigraphs are graphs where multiple edges and edge loops are permitted. The main purpose of this article is to show the versatility of a multigraph approach when analysing social networks. Multigraph data structures are described and it is exemplified how they naturally occur in many contexts but also how they can be constructed by different kinds of aggregation in graphs. Special attention is given to a random multigraph model based on independent edge assignments to sites of vertex pairs and some useful measures of the local and global structure under this model are presented. Further, it is shown how some general measures of simplicity and complexity of multigraphs are easily handled under the present model.