Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Children’s Stories Supporting the Development of Critical Literacy and Intercultural Understanding

This chapter examines the possibilities of applying children’s storybooks in supporting the development of critical literacy as well as intercultural understanding. Valuing and supporting children’s reading is known to provide understanding and empathy towards other human beings. The chapter focuses on theoretical notions related to promoting critical literacies through children’s storybooks, but also includes practical examples of utilizing multicultural children’s stories. The chapter introduces different strategies that parents and teachers can use to support the development of critical literacy, including critical thinking and understanding multiple perspectives. Focus is especially on young children, because they already are capable of moving beyond what is in front of them on the page. Since children’s storybooks offer possibilities for readers to question implicit assumptions about self and others, books can support readers in becoming more culturally aware and sensitive. Consequently, reading storybooks can affect children’s intercultural understanding, and the role of storybooks in children’s moral development – both shaping and changing attitudes – should be seen as transformative.Peer reviewe

I-Louvain: An Attributed Graph Clustering Method

International audienceModularity allows to estimate the quality of a partition into communities of a graph composed of highly interconnected vertices. In this article, we introduce a complementary measure, based on inertia, and specially conceived to evaluate the quality of a partition based on real attributes describing the vertices. We propose also I-Louvain, a graph nodes clustering method which uses our criterion , combined with Newman's modularity, in order to detect communities in attributed graph where real attributes are associated with the vertices. Our experiments show that combining the relational information with the attributes allows to detect the communities more efficiently than using only one type of information. In addition, our method is more robust to data degradation

Vaccine-induced correlate of protection against fatal COVID-19 in older and frail adults during waves of neutralization-resistant variants of concern : an observational study

Background: To inform future preventive measures including repeated vaccinations, we have searched for a clinically useful immune correlate of protection against fatal COVID-19 among nursing homes residents. Methods: We performed repeated capillary blood sampling with analysis of S-binding IgG in an open cohort of nursing home residents in Sweden. We analyzed immunological and registry data from 16 September 2021 to 31 August 2022 with follow-up of deaths to 30 September 2022. The study period included implementation of the 3rd and 4th mRNA monovalent vaccine doses and Omicron virus waves. Findings: A total of 3012 nursing home residents with median age 86 were enrolled. The 3rd mRNA dose elicited a 99-fold relative increase of S-binding IgG in blood and corresponding increase of neutralizing antibodies. The 4th mRNA vaccine dose boosted levels 3.8-fold. Half-life of S-binding IgG was 72 days. A total 528 residents acquired their first SARS-CoV-2 infection after the 3rd or the 4th vaccine dose and the associated 30-day mortality was 9.1%. We found no indication that levels of vaccine-induced antibodies protected against infection with Omicron VOCs. In contrast, the risk of death was inversely correlated to levels of S-directed IgG below the 20th percentile. The death risk plateaued at population average above the lower 35th percentile of S-binding IgG. Interpretation: In the absence of neutralizing antibodies that protect from infection, quantification of S-binding IgG post vaccination may be useful to identify the most vulnerable for fatal COVID-19 among the oldest and frailest. This information is of importance for future strategies to protect vulnerable populations against neutralization resistant variants of concern