On 5 September 2022, the Ms 6.8 Luding earthquake occurred at 29.59°N and 102.08°E in China. To investigate the variations in geomagnetic signals before the earthquake, this study analyzes the geomagnetic data from nine stations around the epicenter. First, we apply the Multi-channel Singular Spectrum Analysis to reconstruct the periodic components of the geomagnetic data from multiple stations. Second, we employ K-means clustering to rule out the possibility of occasional anomalies caused by a single station. Subsequently, we construct a geomagnetic topology network considering the remaining stations. Network centrality is defined as a measure of overall network connectivity, where the higher the correlation between multiple stations, the greater the network centrality. Finally, we examine the network centrality 45 days before and 15 days after the Luding earthquake. The results show that several anomalies in network centrality are extracted about one week before the earthquake. We further validate the significance of the anomalies in terms of time as well as space and verify the utility of the centrality anomalies through the SEA technique. The anomalies are found to have a statistical correlation with the earthquake event. We consider that this study provides a new way and a novel observational perspective for earthquake precursor analysis of ground-based magnetic data.