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The increasing quantity and quality of the publicly available human cerebraldiffusion MRI data make possible the study of the brain as it was unimaginablebefore. The Consensus Connectome Dynamics (CCD) is a remarkable phenomenon thatwas discovered by continuously decreasing the minimum confidence-parameter atthe graphical interface of the Budapest Reference Connectome Server(\url{http://connectome.pitgroup.org}). The Budapest Reference ConnectomeServer depicts the cerebral connections of $n=418$ subjects with afrequency-parameter $k$: For any $k=1,2,...,n$ one can view the graph of theedges that are present in at least $k$ connectomes. If parameter $k$ isdecreased one-by-one from $k=n$ through $k=1$ then more and more edges appearin the graph, since the inclusion condition is relaxed. The surprisingobservation is that the appearance of the edges is far from random: itresembles a growing, complex structure, like a tree or a shrub (visualized on\url{https://www.youtube.com/watch?v=yxlyudPaVUE}). Here we examine therobustness of the CCD phenomenon, and we show that it is almost independent ofthe particular choice of the set of underlying individual connectomes, yieldingthe CCD phenomenon. This result shows that the CCD phenomenon is very likely abiological property of the human brain and not just a property of the data setsexamined. We also present a simulation that well-describes the growth of theCCD structure: in our random graph model a doubly-preferential attachmentdistribution is found to mimic the CCD: a new edge appear with a probabilityproportional to the sum of the degrees of the endpoints of the new edge.

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