Perceived social support can buffer stress, but how it is associated across online social networks at different graph distances remains unclear. Here we show that inferred perceived online social support in a large avatar communication application decays with network distance in a form better described, over the observed range, by a power-decay model than by a single exponential. We linked two-wave survey data from Pigg Party with behavioral logs, trained a random forest to infer perceived support for active users, and regressed Wave 2 scores on Wave 1 scores for users at hop distance $k$, adjusting for baseline support and covariates. Adjusted associations persisted across hops, consistent with power-law-like decay over the observed range. Individual-based simulations indicated that heterogeneous source-specific exponential decay rates can generate heavy-tailed aggregate decay. These results suggest that network position heterogeneity should be considered when characterizing distance-dependent associations among psychosocial states in online communities.
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