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How to Direct the Edges of the Connectomes: Dynamics of the Consensus Connectomes and the Development of the Connections in the Human Brain

The human connectome is the object of an intensive research today. In these graphs, the vertices correspond to the small areas of the gray matter, and two vertices are connected by an edge, if a diffusion-MRI based workflow finds connections between those areas. One main question of the field is discovering the directions of the edges. In a previous work we have reported the construction of the Budapest Reference Connectome Server http://connectome.pitgroup.org from the data recorded in the Human Connectome Project of the NIH. After the server had been published, we recognized a surprising and unforeseen property of it: The server can generate the braingraph of connections that are present in at least $k$ graphs out of the 418, for any value of $k=1,2,...,418$. When the value of $k$ is changed from $k=418$ through 1 by moving a slider at the webserver from right to left, more and more edges appear in the consensus graph. The astonishing observation is that the appearance of the new edges is not random: it is similar to a growing tree. We hypothesize that this movement of the slider in the webserver may copy the development of the connections in the human brain in the following sense: the connections that are present in all subjects are the oldest ones, and those that are present in a decreasing fraction of subjects are gradually the newer connections in the individual brain development. An animation on the phenomenon is available at https://youtu.be/EnWwIf_HNjw. Based on this hypothesis, we can assign directions to the edges of the connectome as follows: Let $G_i$ denote the consensus connectome where each edge is present in at least $i$ graphs. Suppose that vertex $v$ is isolated in $G_{k+1}$, and becomes connected to a vertex $u$ in $G_k$, where $u$ was connected to other vertices already in $G_{k+1}$. Then we direct this $(v,u)$ edge from $v$ to $u$.

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