Cognitive Neurodynamics

, Volume 13, Issue 5, pp 453–460 | Cite as

The frequent subgraphs of the connectome of the human brain

  • Máté Fellner
  • Bálint Varga
  • Vince GrolmuszEmail author
Research Article


In mapping the human structural connectome, we are in a very fortunate situation: one can compute and compare graphs, describing the cerebral connections between the very same, anatomically identified small regions of the gray matter among hundreds of human subjects. The comparison of these graphs has led to numerous recent results, as the (1) discovery that women’s connectomes have deeper and richer connectivity-related graph parameters like those of men, or (2) the description of more and less conservatively connected lobes and cerebral regions, and (3) the discovery of the phenomenon of the consensus connectome dynamics. Today one of the greatest challenges of brain science is the description and modeling of the circuitry of the human brain. For this goal, we need to identify sub-circuits that are present in almost all human subjects and those, which are much less frequent: the former sub-circuits most probably have functions with general importance, the latter sub-circuits are probably related to the individual variability of the brain structure and function. The present contribution describes the frequent connected subgraphs of at most six edges in the human brain. We analyze these frequent graphs and also examine sex differences in these graphs: we demonstrate numerous connected subgraphs that are more frequent in female or male connectomes. While there is no difference in the number of k edge connected subgraphs in males or females for \({\text{k}} = 1\), and for \({\text{k}} = 2\) males have slightly more frequent subgraphs, for \({\text{k}} = 6\) there is a very strong advantage in the case of female braingraphs. Our data source is the public release of the Human Connectome Project, and we are applying the data of 426 human subjects in this study.


Connectome Braingraph Frequent braingraphs Sex differences 



Data were provided in part by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research; and by the McDonnell Center for Systems Neuroscience at Washington University. VG and BV were partially supported by the VEKOP-2.3.2-16-2017-00014 program, supported by the European Union and the State of Hungary, co-financed by the European Regional Development Fund, and the NKFI-126472 and the NKFI-127909 grants of the National Research, Development and Innovation Office of Hungary. BV and MF was supported in part by the EFOP-3.6.3-VEKOP-16-2017-00002 grant, supported by the European Union, co-financed by the European Social Fund.

Author contributions

BV computed braingraphs from the HCP data and created Figs. 1, 2 and 3; MF analyzed braingraphs, invented the frequent braingraph finding extension of the apriori algorithm, contributed Figure 4 and the Supporting material, wrote the “Methods” section, and performed statistical analysis. VG has initiated the study, analyzed data and wrote the paper.

Data availability statement

The data source of this study is Human Connectome Project’s website at (McNab et al. 2013). The connectomes, computed by us can be freely downloaded from (Kerepesi et al. 2017). The large supporting tables can be downloaded from

Compliance with ethical standards

Conflict of interest

The authors declare no conflicts of interest.

Supplementary material

11571_2019_9535_MOESM1_ESM.pdf (5.5 mb)
Supplementary material 1 (pdf 5645 KB)


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.PIT Bioinformatics GroupEötvös UniversityBudapestHungary
  2. 2.Uratim Ltd.BudapestHungary

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