In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has made possible to detect the central areas of a neural system, and to identify its building blocks by looking at overabundant small subgraphs, known as motifs. However, network analysis of the brain has so far mainly focused on anatomical and functional networks as separate entities. The recently developed mathematical framework of multi-layer networks allows to perform an analysis of the human brain where the structural and functional layers are considered together. In this work we describe how to classify the subgraphs of a multiplex network, and we extend motif analysis to networks with an arbitrary number of layers. We then extract multi-layer motifs in brain networks of healthy subjects by considering networks with two layers, anatomical and functional, respectively obtained from diffusion and functional magnetic resonance imaging. Results indicate that subgraphs in which the presence of a physical connection between brain areas (links at the structural layer) coexists with a non-trivial positive correlation in their activities are statistically overabundant. Finally, we investigate the existence of a reinforcement mechanism between the two layers by looking at how the probability to find a link in one layer depends on the intensity of the connection in the other one. Showing that functional connectivity is non-trivially constrained by the underlying anatomical network, our work contributes to a better understanding of the interplay between structure and function in the human brain.
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，皇家理工学院和斯德哥尔摩大学）；Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University（复杂网络与系统研究中心，卢迪信息学、计算与工程学院，印第安纳大学）；School of Mathematical Sciences, Queen Mary University of London（数学科学学院，伦敦玛丽女王大学）
