Rich-club reorganization of white matter structural network in schizophrenia patients with auditory verbal hallucinations following 1 Hz rTMS treatment.

"appendix a supplementary data the following are the supplementary data to this article: supplementary figure 1 supplementary data 1 supplementary data 2 data availability data will be made available on request."

"Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper."

"We gratefully acknowledge the invaluable suggestions provided by the reviewers, which significantly enhanced the quality of this work. This research was supported by the 10.13039/501100001809National Natural Science Foundation of China (No. 61806210 and No.82330043), 10.13039/501100015401Key Research and Development Program of Shaanxi Province (No. 2023-ZDLSF-07), Postdoctoral Science Foundation of China (No. 2019M653963), and 10.13039/100006831Air Force Medical University Everest project (No. 2020cyjhfp). Muzhen Guan: Conceptualization, Data curation, Formal analysis, Investigation, Writing – original draft, Writing – review & editing. Yuanjun Xie: Conceptualization, Data curation, Methodology, Investigation, Formal analysis, Validation, Visual, Writing – original draft, Writing – review & editing. Chenxi Li: Formal analysis, Methodology, Software, Writing – original draft, Writing – review & editing. Tian Zhang: Formal analysis, Methodology, Software, Visualization. Chaozong Ma: Formal analysis, Methodology, Software, Visualization. Zhongheng Wang: Data curation, Investigation, Resources, Validation, Visualization. Zhujing Ma: Formal analysis, Investigation, Methodology, Software, Validation, Visualization. Huaning Wang: Conceptualization, Funding acquisition, Supervision. Peng Fang: Conceptualization, Funding acquisition, Supervision."

"All participants provided written informed consent prior to this study. This study was approved by the Medical Ethics Committee of the Xijing Hospital and was registered in the Chinese Clinical Trial Register (https://www.chictr.org/cn/; registration number: ChiCTR2100041876)."