### Abstract

A cycle in a graph 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. While the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, enumerating cycles in the network is not easy and often requires brute force enumerations. In this study, we present a new scalable algorithm for enumerating the number of cycles in the network. We show that the number of cycles is monotonically decreasing with respect to the filtration values during graph filtration. We further develop a new statistical inference framework for determining the significance of the number of cycles. The methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the functional human brain network.

Original language | English (US) |
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Title of host publication | ISBI 2019 - 2019 IEEE International Symposium on Biomedical Imaging |

Publisher | IEEE Computer Society |

Pages | 113-116 |

Number of pages | 4 |

ISBN (Electronic) | 9781538636411 |

DOIs | |

State | Published - Apr 2019 |

Externally published | Yes |

Event | 16th IEEE International Symposium on Biomedical Imaging, ISBI 2019 - Venice, Italy Duration: Apr 8 2019 → Apr 11 2019 |

### Publication series

Name | Proceedings - International Symposium on Biomedical Imaging |
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Volume | 2019-April |

ISSN (Print) | 1945-7928 |

ISSN (Electronic) | 1945-8452 |

### Conference

Conference | 16th IEEE International Symposium on Biomedical Imaging, ISBI 2019 |
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Country | Italy |

City | Venice |

Period | 4/8/19 → 4/11/19 |

### Fingerprint

### ASJC Scopus subject areas

- Biomedical Engineering
- Radiology Nuclear Medicine and imaging

### Cite this

*ISBI 2019 - 2019 IEEE International Symposium on Biomedical Imaging*(pp. 113-116). [8759222] (Proceedings - International Symposium on Biomedical Imaging; Vol. 2019-April). IEEE Computer Society. https://doi.org/10.1109/ISBI.2019.8759222

**Statistical inference on the number of cycles in brain networks.** / Chung, Moo K.; Huang, Shih Gu; Gritsenko, Andrey; Shen, Li; Lee, Hyekyoung.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ISBI 2019 - 2019 IEEE International Symposium on Biomedical Imaging.*, 8759222, Proceedings - International Symposium on Biomedical Imaging, vol. 2019-April, IEEE Computer Society, pp. 113-116, 16th IEEE International Symposium on Biomedical Imaging, ISBI 2019, Venice, Italy, 4/8/19. https://doi.org/10.1109/ISBI.2019.8759222

}

TY - GEN

T1 - Statistical inference on the number of cycles in brain networks

AU - Chung, Moo K.

AU - Huang, Shih Gu

AU - Gritsenko, Andrey

AU - Shen, Li

AU - Lee, Hyekyoung

PY - 2019/4

Y1 - 2019/4

N2 - A cycle in a graph 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. While the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, enumerating cycles in the network is not easy and often requires brute force enumerations. In this study, we present a new scalable algorithm for enumerating the number of cycles in the network. We show that the number of cycles is monotonically decreasing with respect to the filtration values during graph filtration. We further develop a new statistical inference framework for determining the significance of the number of cycles. The methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the functional human brain network.

AB - A cycle in a graph 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. While the number of connected components represents the integration of the brain network, the number of cycles represents how strong the integration is. However, enumerating cycles in the network is not easy and often requires brute force enumerations. In this study, we present a new scalable algorithm for enumerating the number of cycles in the network. We show that the number of cycles is monotonically decreasing with respect to the filtration values during graph filtration. We further develop a new statistical inference framework for determining the significance of the number of cycles. The methods are applied in determining if the number of cycles is a statistically significant heritable network feature in the functional human brain network.

UR - http://www.scopus.com/inward/record.url?scp=85073901475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85073901475&partnerID=8YFLogxK

U2 - 10.1109/ISBI.2019.8759222

DO - 10.1109/ISBI.2019.8759222

M3 - Conference contribution

AN - SCOPUS:85073901475

T3 - Proceedings - International Symposium on Biomedical Imaging

SP - 113

EP - 116

BT - ISBI 2019 - 2019 IEEE International Symposium on Biomedical Imaging

PB - IEEE Computer Society

ER -