Epileptic seizures and the interictal epileptiform discharges both have similar waveforms. And a method to effectively extract features that can be used to distinguish seizures is of crucial importance both in theory and clinical practice. We constructed state transfer networks by using visibility graphlet at multiple sampling intervals and analyzed network features. We found that the characteristics waveforms in ictal periods were more robust with various sampling intervals, and those feature network structures did not change easily in the range of the smaller sampling intervals. Inversely, the feature network structures of interictal epileptiform discharges were stable in range of relatively larger sampling intervals. Furthermore, the feature nodes in networks during ictal periods showed long-term correlation along the process, and played an important role in regulating system behavior. For stereo-electroencephalography at around 500 Hz, the greatest difference between ictal and the interictal epileptiform occurred at the sampling interval around 0.032 s. In conclusion, this study effectively reveals the correlation between the features of pathological changes in brain system and the multiple sampling intervals, which holds potential application value in clinical diagnosis for identifying, classifying, and predicting epilepsy.