The Delta variant of COVID-19 has been found to be extremely difficult to contain worldwide. The complex dynamics of human mobility and the variable intensity of local outbreaks make measuring the factors of COVID-19 transmission a challenge. The inter-suburb road connection details provide a reliable proxy of the moving options for people between suburbs for a given region. By using such data from Greater Sydney, Australia, this study explored the impact of suburban road networks on two COVID-19-related outcomes measures. The first measure is COVID-19 vulnerability, which gives a low score to a more vulnerable suburb. A suburb is more vulnerable if it has the first COVID-19 case earlier and vice versa. The second measure is COVID-19 severity, which is proportionate to the number of COVID-19-positive cases for a suburb. To analyze the suburban road network, we considered four centrality measures (degree, closeness, betweenness and eigenvector) and core–periphery structure. We found that the degree centrality measure of the suburban road network was a strong and statistically significant predictor for both COVID-19 vulnerability and severity. Closeness centrality and eigenvector centrality were also statistically significant predictors for COVID-19 vulnerability and severity, respectively. The findings of this study could provide practical insights to stakeholders and policymakers to develop timely strategies and policies to prevent and contain any highly infectious pandemics, including the Delta variant of COVID-19.