Measure of Node Similarity in Multilayer Networks

The weight of links in a network is often related to the similarity of thenodes. Here, we introduce a simple tunable measure for analysing the similarityof nodes across different link weights. In particular, we use the measure toanalyze homophily in a group of 659 freshman students at a large university.Our analysis is based on data obtained using smartphones equipped with customdata collection software, complemented by questionnaire-based data. The networkof social contacts is represented as a weighted multilayer network constructedfrom different channels of telecommunication as well as data on face-to-facecontacts. We find that even strongly connected individuals are not more similarwith respect to basic personality traits than randomly chosen pairs ofindividuals. In contrast, several socio-demographics variables have asignificant degree of similarity. We further observe that similarity might bepresent in one layer of the multilayer network and simultaneously be absent inthe other layers. For a variable such as gender, our measure reveals atransition from similarity between nodes connected with links of relatively lowweight to dis-similarity for the nodes connected by the strongest links. Wefinally analyze the overlap between layers in the network for different levelsof acquaintanceships.