Objectives The purpose of this study was to (1) explore the changes in topological properties of static and dynamic brain functional networks after nasopharyngeal carcinoma (NPC) radiotherapy (RT) using rs-fMRI and graph theoretical analysis, (2) explore the correlation between cognitive function and changes in brain function, and (3) add to the understanding of the pathogenesis of radiation brain injury (RBI). Methods Fifty-four patients were divided into 3 groups according to time after RT: PT1 (0-6 months); PT2 (> 6 to <= 12 months); and PT3 (> 12 months). 29 normal controls (NCs) were included. The subjects' topological properties were evaluated by graph-theoretic network analysis, the functional connectivity of static functional networks was calculated using network-based statistics, and the dynamic functional network matrix was subjected to cluster analysis. Finally, correlation analyses were conducted to explore the relationship between the altered network parameters and cognitive function. Results Assortativity, hierarchy, and network efficiency were significantly abnormal in the PT1 group compared with the NC or PT3 group. The small-world variance in the PT3 group was smaller than that in NCs. The Nodal ClustCoeff of Postcentral_R in the PT2 group was significantly smaller than that in PT3 and NC groups. Functional connectivities were significantly reduced in the patient groups. Most of the functional connectivities of the middle temporal gyrus (MTG) were shown to be significantly reduced in all three patient groups. Most of the functional connectivities of the insula showed significantly reduced in the PT1 and PT3 groups, and most of the functional connectivities in brain regions such as frontal and parietal lobes showed significantly reduced in the PT2 and PT3 groups. These abnormal functional connectivities were correlated with scores on multiple scales that primarily assessed memory, executive ability, and overall cognitive function. The frequency F of occurrence of various states in each subject differed significantly, and the interaction effect of group and state was significant. Conclusion The disruption of static and dynamic functional network stability, reduced network efficiency and reduced functional connectivity may be potential biomarkers of RBI. Our findings may provide new insights into the pathogenesis of RBI from the perspective of functional networks.