Abstract
Centrality measures are used in network science to assess the centrality of vertices or the position they occupy in a network. There are a large number of centrality measures according to some criterion. However, the generalizations of the most well-known centrality measures for weighted networks, degree centrality, closeness centrality and betweenness centrality have solely assumed the edge weights to be constants. This article proposes a methodology to generalize degree, closeness and betweenness centralities taking into account the variability of edge weights in the form of closed intervals (interval-weighted networks, IWN). We apply our centrality measures approach to two real-world IWN. The first is a commuter network in mainland Portugal, between the 23 NUTS 3 Regions. The second focuses on annual merchandise trade between 28 European countries, from 2003 to 2015.

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
IntroductionWilson's disease (WD) is associated with a variety of movement disorders and progressive neurological dysfunction. The aim of this study was to correlate baseline brain magnetic resonance imaging (MRI) features with clinical phenotype and long-term outcomes in chronically treated WD patients.MethodsPatients were retrospectively selected from an institutional database. Two experienced neuroradiologists reviewed baseline brain MRI. Functional assessment was performed using the World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0) scale, and disease severity was classified using the Global Assessment Scale for Wilson's Disease (GASWD).ResultsOf 27 patients selected, 14 were female (51.9%), with a mean (standard deviation [SD]) age at onset of 19.5 (7.1) years. Neurological symptoms developed in 22 patients (81.5%), with hyperkinetic symptoms being the most common (70.4%). Baseline brain MRI showed abnormal findings in 18 cases (66.7%), including T2 hyperintensities in 59.3% and atrophy in 29.6%. After a mean (SD) follow-up of 20.9 (11.0) years, WD patients had a mean score of 19.2 (10.2) on WHODAS 2.0 and 6.4 (5.7) on GASWD. The presence of hyperkinetic symptoms correlated with putaminal T2 hyperintensities (p = 0.003), putaminal T2 hypointensities (p = 0.009), and mesencephalic T2 hyperintensities (p = 0.009). Increased functional disability was associated with brain atrophy (p = 0.007), diffusion abnormalities (p = 0.013), and burden of T2 hyperintensities (p = 0.002). A stepwise regression model identified atrophy as a predictor of increased WHODAS 2.0 (p = 0.023) and GASWD (p = 0.007) scores.ConclusionsAtrophy and, to a lesser extent, deep T2 hyperintensity are associated with functional disability and disease severity in long-term follow-up of WD patients.

Abstract
Increasing scientific evidence supports an association between alexithymia and psychoactive substance use. This study explores alexithymia´s expression in sample of long-term drug users, undergoing outpatient treatment in public health units in Oporto, Portugal, as well as its´ association with social demographic risk factors. Data was collected from a sample of 90 adults, participants, mainly men (n=90; 87%), considered to be old consumers (81% with a age>40 years), with a mean age of 46.1 years (SD=8.3; range=21–64).Two instruments were used: a sociodemographic questionnaire and the 20-item Toronto Alexithymia Scale (TAS-20). More than 51.1% of the individuals were alexithymic, indicating a high prevalence of deficits in emotional awareness. The treatment period varied from 0 to 15 years, included a medication in 55% of cases, mostly methadone (83%). This profile illustrates the gradual aging of the long-term users of illicit drugs and alcohol with a clear diagnosis of an emotional disorder. Therefore, clinicians who develop treatment strategies may want to take into account the likelihood that many of their patients may be alexithymic; in being so, they should integrate specific psychotherapeutic techniques that promote both the identification and the differentiation in emotionally dysfunctional patients.

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.