A Hierarchical Brain Network Model Based on the K-Shell Decomposition Algorithm

Abstract

The human brain is a complicated network which has some conflicted properties simultaneously such as robustness and vulnerability. Early researchers try to explore the phenomenon mainly focused their attention on the graphical properties of the node itself, such as degree and betweenness etc., but ignored the affection of the neighbors. This research suggested a perspective from the topological structure of the complex network to explore the paradoxical phenomenon. We introduced the K-shell decomposition algorithm to explore the structure of the brain network and the characteristics of nodes in it. Such method considers both the properties of the node itself and the affection of neighbors might inflict. Based on the algorithm, we generated a hierarchical brain network model. According to this model, the brain network has three components: the nucleus with the densest connection within it, the giant component, the nodes in it connect with each other but do not reach to the nucleus; the isolated nodes which solely connect to other parts of the network through the nucleus. Such ‘medusa-like’ shape was similar to the internet which promises that only when the nucleus had been destroyed, the robustness of the network would be damaged. Based on such structure, we hypothesize that the brain regions which belong to the nucleus could be considered as biomarkers of early detection for some neurodegenerative diseases, for these diseases only destroyed few brain regions that could cause the brain dysfunction to the patients, at the same time, such organization also suggests there are two different information delivery paths for the different cognitive tasks.