Community recovery from hazards and crises occurs through various diffusion processes within social and spatial networks of communities. Existing knowledge regarding the diffusion of recovery in community socio-spatial networks, however, is rather limited. To bridge this gap, in this study, we created a network diffusion model to characterize the unfolding of population activity recovery in spatial networks of communities. Using data related to population activity recovery durations calculated from location-based data in the context of 2017 Hurricane Harvey in the Houston area, we parameterized the threshold-based network diffusion model and evaluated the extent of homogeneity in spatial effects. Then we implemented the network diffusion model along with the genetic algorithm to simulate and identify recovery multipliers. The results show that the spatial effects of recovery are rather heterogeneous across spatial areas; some spatial areas demonstrate a greater spatial effect (spatial interdependence) in their recovery compared with others. Also, the results show that low-income areas demonstrate a greater spatial effect in their recovery. The greater spatial effects in recovery of low-income areas imply more reliance on resources and facilities of neighboring areas and also explain the existence of slow recovery hotspots in areas where socially vulnerable populations reside. Also, the results show that low-income and minority areas are community recovery multipliers; the faster the recovery of these recovery multipliers; the faster the recovery of the entire community. Hence, prioritizing these areas for recovery resource allocation could expedite the recovery of the overall community and promote recovery equality and equity.