This study evaluates the scale-free network assumption commonly used in COVID-19 epidemiology, using empirical social network data from SARS-CoV-2 Delta variant molecular local clusters in Houston, Texas. We constructed genome-informed social networks from contact and co-residence data, tested them for scale-free power-law distributions that imply highly connected hubs, and compared them to alternative models (exponential, log-normal, power-law with exponential cutoff, and Weibull) that suggest more evenly distributed network connections. Although the power-law model failed the goodness of fit test, after incorporating social network ties, the power-law model was at least as good as, if not better than, the alternatives, implying the presence of both hub and non-hub mechanisms in local SARS-CoV-2 transmission. These findings enhance our understanding of the complex social interactions that drive SARS-CoV-2 transmission, thereby informing more effective public health interventions.