Measure of Node Similarity in Multilayer Networks

Abstract

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

arXiv comment12 pages, 4 figures

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• Multilayer Networks
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• Gender homophily from spatial behavior in a primary school: a sociometric study
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• Layer Communities in Multiplex Networks
• Are the different layers of a social network conveying the same information?
• Dose-response functions and surrogate models for exploring social contagion in the Copenhagen Networks Study
• Role Similarity Metric Based on Spanning Rooted Forest
• Node similarity distribution of complex networks and its application in link prediction