The COVID-19 pandemic triggered an unprecedented level of restrictive measures globally. Most countries resorted to lockdowns at some point to buy the much-needed time for flattening the curve and scaling up vaccination and treatment capacity. Although lockdowns, social distancing and business closures generally slowed the case growth, there is a growing concern about these restrictions' social, economic and psychological impact, especially on the disadvantaged and poorer segments of society. While we are all in this together, these segments often take the heavier toll of the pandemic and face harsher restrictions or get blamed for community transmission. This study proposes a road-network-based networked approach to model mobility patterns between localities during lockdown stages. It utilises a panel regression method to analyse the effects of mobility in transmitting COVID-19 in an Australian context, together with a close look at a suburban population’s characteristics like their age, income and education. Firstly, we attempt to model how the local road networks between the neighbouring suburbs (i.e., neighbourhood measure) and current infection count affect the case growth and how they differ between delta and omicron variants. We use a geographic information system, population and infection data to measure road connections, mobility and transmission probability across the suburbs. We then looked at three socio-demographic variables: age, education and income and explored how they moderate independent and dependent variables (infection rates and neighbourhood measures). The result shows strong model performance to predict infection rate based on neighbourhood road connection. However, apart from age in the delta variant context, the other variables (income and education level) do not seem to moderate the relationship between infection rate and neighbourhood measure. The results indicate that suburbs with a more socio-economically disadvantaged population do not necessarily contribute to more community transmission. The study findings could be potentially helpful for stakeholders in tailoring any health decision for future pandemics.