Characterization of brain networks by diffusion MRI (dMRI) has rapidly evolved, and there are ongoing movements toward data sharing and multi-center studies. To extract meaningful information from multi-center data, methods to correct for the bias caused by scanner differences, that is, harmonization, are urgently needed. In this work, we report the cross-scanner differences in structural network analyses using data from nine traveling subjects (four males and five females, 21–49 years-old) who underwent scanning using four 3T scanners (public database available from the Brain/MINDS Beyond Human Brain MRI project (http://mriportal.umin.jp/)). The reliability and reproducibility were compared to those of data from another set of four subjects (all males, 29–42 years-old) who underwent scan-rescan (interval, 105–147 days) with the same scanner as well as scan-rescan data from the Human Connectome Project database. The results demonstrated that the reliability of the edge weights and graph theory metrics was lower for data including different scanners, compared to the scan-rescan with the same scanner. Besides, systematic differences between scanners were observed, indicating the risk of bias in comparing networks obtained from different scanners directly. We further demonstrate that it is feasible to reduce inter-scanner variabilities while preserving the inter-subject differences among healthy individuals by modeling the scanner effects at the level of network matrices, when traveling-subject data are available for calibration between scanners. The present data and results are expected to serve as a basis for developing and evaluating novel harmonization methods.