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.

Background: It is well known that the university period is an important stage for young adults, involving significant academic and psychosocial adjustments. Students with greater Mental Health Literacy (MHL), which is defined as the knowledge, beliefs, and skills individuals have regarding mental health and mental illness, are better able to identify difficulties, seek help, and adopt healthier coping strategies. This study aims to describe the MHL levels of undergraduate health students and identify associated factors related to academic life, mental health and psychological state. Methods: A cross-sectional, self-administered, web-based survey was conducted using a non-probability sampling strategy among undergraduate students in health-related degrees at a Portuguese higher-education institution. Data was collected using a general characterization questionnaire and the following instruments: MHL Questionnaire, Academic Life Satisfaction, Subjective Happiness Scale, Psychological Well-Being Scale (PWBS), and Depression Anxiety Stress Scale. Bivariate and linear regression analyses were employed to identify factors associated with MHL. Results: A total of 306 students (79% female, mean age = 21.6 years; 59% nursing students) participated. The median MHL score was 70 (range: 30–80). The linear regression model explained 17.5% of the variance in MHL. Higher MHL levels were associated with having the course as a first choice, holding a previous degree, reporting taking psychotropic medication use (which may reflect previous mental health service utilization), and higher levels of psychological well-being. Conclusions: This study provides evidence on factors associated with MHL among undergraduate health students, suggesting that higher MHL is associated with greater psychological well-being, highlighting the potential importance of integrating strategies to promote MHL and psychological well-being in health and nursing education. However, these findings should be interpreted with caution due to the single-institution convenience sample, potential self-selection and reporting biases, and cross-sectional design, which limits causal inferences.

Background: Cognitive Impairment (CI) is a growing public health problem among the older population, with well‐established risk factors. However, the role of psychosocial predictors still needs to be clarified. This study aimed to analyze whether psychosocial factors may be predictors of CI in older persons.Method: In the framework of “Porto. Importa‐se” longitudinal project, this study included older persons (≥70y.o. living alone and couples ≥75y.o.), living in social housing in Porto city, Portugal. The research protocol included: Six‐item Cognitive Impairment Test (CI), Barthel and Lawton Index (Basic/Instrumental Activities of Daily Living‐BADLs/IADLs), Geriatric Depression Scale‐15 (depressive symptoms) and Lubben Social Network Scale‐6 (social isolation). Loneliness was assessed with a categorical question: Do you feel lonely?. A logistic regression analysis was conducted to identify predictors of CI. Odds Ratio (OR) and its 95% Confidence Interval (95%CI) were calculated. A p<0.05 was considered statistically significant.Result: Of the 1213 older persons (mean age 81±5.7) included, most were female (74%) and 36% had low education level (<4years). About 11% were severely dependent on IADLs and 27% presented CI. Around 35% of participants were at risk of social isolation, 54% reported loneliness and 48% showed depressive symptoms.The logistic regression model was statistically significant [X²(5,N = 1213) = 148.596,p<.001], explaining 19.7%(Nagelkerke R²) of variance in CI (correctly classified 77% of cases). The adjusted model had a moderate sensitivity (63%) and specificity (78%). The oldest persons (≥80 years old) were 1.77 as likely to have CI than younger (OR = 1.77, 95%CI[1.3, 2.4]). Those with less education (<4years) were 0.26 times as likely to present CI than reference group (≥4years) (OR = 0.26, 95%CI[0.2, 0.4]) and females 1.5 times more than males (OR = 1.50, 95%CI[1.0, 2.2]). Older persons at risk of social isolation were 1.85 as likely to have CI (OR = 1.85, 95%CI[1.4, 2.5] and those with depressive symptoms were 1.39 likely to present CI (OR = 1.39, 95%CI[1.0, 1.9]).Conclusion: Older age, female gender, low education, depressive symptoms and social isolation were predictors of CI. The existence of potentially modifiable factors (e.g., social isolation, depression), means that CI prevention is possible through the implementation of effective individual and community‐level interventions, aiming to protect older persons from CI.

Home hospitalization is an alternative to conventional inpatient care, allowing hospital-level treatment to be delivered at home with clinical complexity comparable to that of the hospital setting. In this model, the informal caregiver assumes a central role in ensuring continuity and monitoring of care, often experiencing high physical, emotional, and social demands. This study aimed to describe the burden levels of informal caregivers of patients receiving home hospitalization and to analyze their association with sociodemographic characteristics and perceptions of support from health services.A cross-sectional study was conducted with caregivers from a home hospitalization service of a university hospital in northern Portugal, using a sociodemographic and clinical characterization protocol and the Zarit Burden Interview. The sample included 76 caregivers [78.9% female; mean age = 61.8 years (SD = 13)], with 59% presenting caregiver burden and 42.1% presenting severe burden. Women showed significantly higher levels in the dimension “Expectations regarding caregiving” (p = 0.047). Caregivers who reported difficulties due to the COVID-19 pandemic presented higher burden in “Perceived self-efficacy” (p = 0.044).The results showed that these caregivers experience substantial levels of burden, reinforcing the need for early identification of such situations, as well as the development and implementation of empowerment strategies and structured support interventions, including psychosocial support and continuous follow-up. These measures are essential not only to improve the quality of care provided but also to promote caregivers’ well-being and autonomy.