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Adjacency relations for social network analysis have usually been tackled in their bidimensional form, in the sense that relations are computed over pairs of objects. Nevertheless, this paper considers the bidimensional case as restrictive and it proposes an approach where the dimension of the analysis is not limited to binary relations. With the aid of fuzzy logic and OWA operators, it is showed that the interpretation of m-ary adjacency relations is the same of binary relations and therefore they can consistently be employed in social network analysis and some novel results be derived. Besides justifying the use of m-ary relations, the paper proposes a way to characterize them and, eventually, it will provide the reader with an example section.