Measure of Node Similarity in Multilayer Networks

TL;DR

This paper introduces a tunable measure for assessing node similarity across different link weights in multilayer networks, applied to social contact data of university students, revealing complex patterns of similarity and dissimilarity.

Contribution

The paper presents a novel, adjustable similarity measure for multilayer networks and demonstrates its application to real-world social contact data, uncovering nuanced similarity patterns.

Findings

Strongly connected individuals are not more similar in personality traits.

Socio-demographic variables show significant similarity.

Similarity varies across different network layers and link weights.

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.