Exact topological inference of the resting-state brain networks in twins

Moo K. Chung, Hyekyoung Lee, Alex Di Christofano, Hernando Ombao, Victor Solo

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


A cycle in a brain network is a subset of a connected component with redundant additional connections. If there are many cycles in a connected component, the connected component is more densely connected. Whereas the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, it is unclear how to perform statistical inference on the number of cycles in the brain network. In this study, we present a new statistical inference framework for determining the significance of the number of cycles through the Kolmogorov-Smirnov (KS) distance, which was recently introduced to measure the similarity between networks across different filtration values by using the zeroth Betti number. In this paper, we show how to extend the method to the first Betti number, which measures the number of cycles. The performance analysis was conducted using the random network simulations with ground truths. By using a twin imaging study, which provides biological ground truth, the methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the resting-state functional connectivity in 217 twins obtained from the Human Connectome Project. The MATLAB codes as well as the connectivity matrices used in generating results are provided at http://www.stat.wisc.edu/~mchung/TDA.
Original languageEnglish (US)
Pages (from-to)674-694
Number of pages21
JournalNetwork Neuroscience
Issue number3
StatePublished - Apr 24 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Moo Chung, National Institutes of Health (http://dx.doi.org/10.13039/100000002), Award ID: EB022856. Hyekyoung Lee, National Research Foundation of Korea (http://dx.doi.org/10.13039/501100003725), Award ID: NRF-2016R1D1A1B03935463.


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