Evaluating relevance and redundancy to quantify how binary node metadata interplay with the network structure.

Networks are real systems modelled through mathematical objects made up of nodes and links arranged into peculiar and deliberate (or partially deliberate) topologies. Studying these real-world topologies allows for several properties of interest to be revealed. In real networks, nodes are also identified by a certain number of non-structural features or metadata. Given the current possibility of collecting massive quantity of such metadata, it becomes crucial to identify automatically which are the most relevant for the observed structure. We propose a new method that, independently from the network size, is able to not only report the relevance of binary node metadata, but also rank them. Such a method can be applied to networks from any domain, and we apply it in two heterogeneous cases: a temporal network of technology transfer and a protein-protein interaction network. Together with the relevance of node metadata, we investigate the redundancy of these metadata displaying by the results on a Redundancy-Relevance diagram, which is able to highlight the differences among vectors of metadata from both a structural and a non-structural point of view. The obtained results provide insights of a practical nature into the importance of the observed node metadata for the actual network structure.