The Robustness and the Doubly-Preferential Attachment Simulation of the Consensus Connectome Dynamics of the Human Brain

Abstract: The increasing quantity and quality of the publicly available human cerebral diffusion MRI data make possible the study of the brain as it was unimaginable before. The Consensus Connectome Dynamics (CCD) is a remarkable phenomenon that was discovered by continuously decreasing the minimum confidence-parameter at the graphical interface of the Budapest Reference Connectome Server (\url{http://connectome.pitgroup.org}). The Budapest Reference Connectome Server depicts the cerebral connections of $n=418$ subjects with a frequency-parameter $k$: For any $k=1,2,...,n$ one can view the graph of the edges that are present in at least $k$ connectomes. If parameter $k$ is decreased one-by-one from $k=n$ through $k=1$ then more and more edges appear in the graph, since the inclusion condition is relaxed. The surprising observation is that the appearance of the edges is far from random: it resembles a growing, complex structure, like a tree or a shrub (visualized on \url{https://www.youtube.com/watch?v=yxlyudPaVUE}). Here we examine the robustness of the CCD phenomenon, and we show that it is almost independent of the particular choice of the set of underlying individual connectomes, yielding the CCD phenomenon. This result shows that the CCD phenomenon is very likely a biological property of the human brain and not just a property of the data sets examined. We also present a simulation that well-describes the growth of the CCD structure: in our random graph model a doubly-preferential attachment distribution is found to mimic the CCD: a new edge appear with a probability proportional to the sum of the degrees of the endpoints of the new edge.