The pursuit of hubbiness: analysis of hubs in large multidimensional networks

Hubs are highly connected nodes within a network. In complex network analysis, hubs have been widely studied, and are at the basis of many tasks, such as web search and epidemic outbreak detection. In reality, networks are often multidimensional, i.e., there can exist multiple connections between any pair of nodes. In this setting, the concept of hub depends on the multiple dimensions of the network, whose interplay becomes crucial for the connectedness of a node. In this paper, we characterize multidimensional hubs. We consider the multidimensional generalization of the degree and introduce a new class of measures, that we call Dimension Relevance, aimed at analyzing the importance of different dimensions for the hubbiness of a node. We assess the meaningfulness of our measures by comparing them on real networks and null models, then we study the interplay among dimensions and their effect on node connectivity. Our findings show that: (i) multidimensional hubs do exist and their characterization yields interesting insights and (ii) it is possible to detect the most influential dimensions that cause the different hub behaviors. We demonstrate the usefulness of multidimensional analysis in three real world domains: detection of ambiguous query terms in a word-word query log network, outlier detection in a social network, and temporal analysis of behaviors in a co-authorship network.