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A complete characterization of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use minimum spanning trees (MSTs) to explore the effect of correlations between link weights and network topology on scale-free networks. Solely by changing the nature of the correlations between weights and network topology, the structure of the MSTs can change from scale-free to exponential. Additionally, for some choices of weightdoi:10.1209/epl/i2005-10232-x fatcat:nrnmqktw3naqnldhjuepwgjllm