The human braingraph or the connectome is the object of an intensive research today. The advantave of the graph-approach to brain science is that the rich structures, algorithms and definitions of graph theory can be applied to the anatomical networks of the connections fo the human brain. In these graphs, the vertices correspond to the small (1-1.5 cm2) areas of the gray matter, and two vertices are connected by an edge, if a diffusion-MRI based workflow finds fibers of axons, running between those small grey matter areas in the white matter of the brain. One main question of the field today is discovering the directions of the connections between the small grey matter areas. In a previous work we have reported the construction of the Budapest Reference Connectome Server from the data recorded in the Human Connectome Project of the NIH. The server generates the consensus braingraph of 96 subjects in Version 2, and of 418 subjects in Version 3, according to selectable parameters. After the Budapest Reference Connectome Server had been published, we recognized a surprising and unforseen property of the server. 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 teh webserver from right to left, certainly more and more edges appera in the consensus graph. The astonishin observation is that the appearance of the new edges is not random: it is similar to a growing shrub. We refer to this phenomenon as the Consensus Connectome Dynamics. We hypothesise 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 conncetions that are present in all subjects are the oldest ones, and those that are present onlu in a decreasing fraction of the subjects are gradually the newer connections in the individual brain development. An animation on the phenomenon is available at https://youtu.be/yxlyudPaVUE. Based on this observation and the related hypothesis, we can assign directions to some of the edges of the connectome as follows: Let Gk denote the consensus connectome where each edge is present in at least k+1 graphs, and let Gk denote the consensus connectome where each edge is present in at least k graphs. Suppose that vertex v is not connected to any other vertices in Gk+1, and becomes connected to a vertex u in Gk, where u was connected to other vertices already in Gk+1. Then we direct this (v,u) edge from v to u.
Kerepesi, C., Szalkai, B., Varga, B., & Grolmusz, V. (2016). How to direct the edges of the connectomes: Dynamics of the consensus connectomes and the development of the connections in the human brain. PLoS ONE, 11(6). https://doi.org/10.1371/journal.pone.0158680