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where g is the collection of all sites connected to X through drainage directions. The theorem predicts that, for efficient drainage basins, a log-log plot of C versus A should have a slope of 3/2 because D = 2 and river networks in nature are known to be efficient and directed. Our observational data (Fig. 2) are found to agree with the predictions over five decades of scales. Our general results should be applicable to a wide variety of distributed networks including the flow of water, blood, sewage, food, air and electrical currents. Even though the specific details vary significantly, the novel behaviour built into efficient transportation networks provides a unified framework underlying the allometric scaling of diverse systems. |
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