Abstract
In this paper we introduce and develop the concept of interval-weighted networks (IWN), a novel approach in Social Network Analysis, where the edge weights are represented by closed intervals composed with precise information, comprehending intrinsic variability. We extend IWN for both Newman's modularity and modularity gain and the Louvain algorithm, considering a tabular representation of networks by contingency tables. We apply our methodology to two real-world IWN. The first is a commuter network in mainland Portugal, between the twenty three NUTS 3 Regions (IWCN). The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015 (IWTN). The optimal partition of geographic locations (regions or countries) is developed and compared using two new different approaches, designated as Classic Louvain and Hybrid Louvain , which allow taking into account the variability observed in the original network, thereby minimizing the loss of information present in the raw data. Our findings suggest the division of the twenty three Portuguese regions in three main communities for the IWCN and between two to three country communities for the IWTN. However, we find different geographical partitions according to the community detection methodology used. This analysis can be useful in many real-world applications, since it takes into account that the weights may vary within the ranges, rather than being constant.

Abstract
Luxembourg, known for its immigration history, attracts immigrants to work. This study analyses different immigrant groups in the labour market from 2014 to 2022 by using Labor Force Survey (LFS) data, Symbolic Data Analysis (SDA), and the Monitoring the Evolution of Clusters (MEC) framework. Based on the birthplace and length of residence in Luxembourg, in each year, microdata were aggregated into 21 symbolic objects. They were primarily described by 16 modal variables which are multi-valued variables with a frequency attached to each category. Moreover, clustering using complete linkage and the Chernoff’s distance was applied. The Heuristic Identification of Noisy Variables (HINoV) suggested that with just six variables, objects may be grouped homogeneously. The MEC framework traced temporal relations and transitions between the clusters, revealing some movements across the different years. Results indicate that people from the European Union (EU) and Neighbouring countries have similar profiles while the Portuguese have opposite characteristics. The Luxembourgers are somewhere in between. Profiling people from non-EU countries was challenging. The data and methodology used make it easy to replicate the work in other nations, enabling comparison of results and monitoring to continue in the future.

Abstract