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