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The human connectome is the object of an intensive research today. In thesegraphs, the vertices correspond to the small areas of the gray matter, and twovertices are connected by an edge, if a diffusion-MRI based workflow findsconnections between those areas. One main question of the field is discoveringthe directions of the edges. In a previous work we have reported theconstruction of the Budapest Reference Connectome Serverhttp://connectome.pitgroup.org from the data recorded in the Human ConnectomeProject of the NIH. After the server had been published, we recognized asurprising and unforeseen property of it: The server can generate thebraingraph of connections that are present in at least $k$ graphs out of the418, 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, moreand more edges appear in the consensus graph. The astonishing observation isthat the appearance of the new edges is not random: it is similar to a growingtree. We hypothesize that this movement of the slider in the webserver may copythe 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 thosethat are present in a decreasing fraction of subjects are gradually the newerconnections in the individual brain development. An animation on the phenomenonis available at https://youtu.be/EnWwIf_HNjw. Based on this hypothesis, we canassign directions to the edges of the connectome as follows: Let $G_i$ denotethe 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 avertex $u$ 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 $u$.

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