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All online sharing systems gather data that reflects users' collective behavior and their shared activities. This data can be used to extract different kinds of relationships which can be grouped into layers and which are basic components of the multidimensional social network (MSN) proposed in the paper. The layers are created on the basis of two types of relations between humans, i.e., direct and object-based ones which, respectively, correspond to either social or semantic links between individuals. For better understanding of the complexity of the social network structure, layers and their profiles were identified and studied on two, spanned in time, snapshots of the `Flickr' population. Additionally, for each layer, a separate strength measure was proposed. The experiments on the `Flickr' photo sharing system revealed that the relationships between users result either from semantic links between objects they operate on or from social connections of these users. Moreover, the density of the social network increases in time. The second part of this paper is devoted to building a social recommender system that supports the creation of new relations between users in a multimedia sharing system. Its main goal is to generate personalized suggestions that are continuously adapted to users' needs depending on the personal weights assigned to each layer in the MSN. The conducted experiments confirmed the usefulness of the proposed model.