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The purpose of this work is to advance in the computational study of connectome graphs from a topological point of view. Specifically, starting from a sequence of hypergraphs associated to a brain graph (obtained using the Boundary Scale model, BS2), we analyze the resulting scale-space representation using classical topological features, such as Betti numbers and average node and edge degrees. In this way, the topological information that can be extracted from the original graph is substantially enriched, thus providing an insightful description of the graph from a clinical perspective. To assess the qualitative and quantitative topological information gain of the BS2 model, we carried out an empirical analysis of neuroimaging data using a dataset that contains the connectomes of 96 healthy subjects, 52 women and 44 men, generated from MRI scans in the Human Connectome Project. The results obtained shed light on the differences between these two classes of subjects in terms of neural connectivity.

La mesure en sciences humaines, bien que largement répandue et pratiquée, a mauvaise presse chez les théoriciens et fait souvent figure d’enfant pauvre à côté de la mesure instrumentale qu’on retrouve dans les sciences physiques et biologiques. Les auteurs reprennent le débat, en reformulant la question et en revoyant les concepts de mesure, unité de mesure, étalon, grandeur et échelle. Ils posent quelques balises qui permettent de juger, sans passion ni préconception, la légitimité des mesures, que ce soit pour des tests psychométriques, des examens scolaires ou d’autres types d’indices socioculturels. La perspective générale, bien que critique, reste favorable et optimiste.