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Accurate representation of the physical layer is required for analysis and simulation of multi-hop networking in sensor, ad hoc, and mesh networks. Radio links that are geographically proximate often experience similar environmental shadowing effects and thus have correlated shadowing. This paper presents and analyzes a non-site-specific statistical propagation model which accounts for the correlations that exist in shadow fading between links in multi-hop networks. We describe two measurement campaigns to measure a large number of multi-hop networks in an ensemble of environments. The measurements show statistically significant correlations among shadowing experienced on different links in the network, with correlation coefficients up to 0.33. Finally, we analyze multi-hop paths in three and four node networks using both correlated and independent shadowing models and show that independent shadowing models can underestimate the probability of route failure by a factor of two or greater.