Previous studies have shown that the brain network topology correlates with the cognitive function. However, few studies have investigated the relationship between functional brain networks that process sensory inputs and outputs. In this study, we focus on steady-state paradigms using a periodic visual stimulus, which are increasingly being used in both brain-computer interface (BCI) and cognitive neuroscience researches. Using the graph theoretical analysis, we investigated the relationship between the topology of functional networks entrained by periodic stimuli and steady state visually evoked potentials (SSVEP) using two frequencies and eleven subjects. First, the entire functional network (Network 0) of each frequency for each subject was constructed according to the coherence between electrode pairs. Next, Network 0 was divided into three sub-networks, in which the connection strengths were either significantly (positively for Network 1, negatively for Network 3) or non-significantly (Network 2) correlated with the SSVEP responses. Our results revealed that the SSVEP responses were positively correlated to the mean functional connectivity, clustering coefficient, and global and local efficiencies, while these responses were negatively correlated with the characteristic path length of Networks 0, 1 and 2. Furthermore, the strengths of these connections that significantly correlated with the SSVEP (both positively and negatively) were mainly found to be long-range connections between the parietal-occipital and frontal regions. These results indicate that larger SSVEP responses correspond with better functional network topology structures. This study may provide new insights for understanding brain mechanisms when using SSVEPs as frequency tags.