## Network Homogenization

The homogenization property yields a comparison of resource distribution between the direct and integral flow intensity matrices. Due to the contribution of indirect pathways, it was observed that flow in the integral matrix was more evenly distributed than that in the direct matrix. A statistical comparison of resources distribution can be made by calculating the coefficient of variation of each of the two matrices. For example, the coefficient of variation of the direct flow intensity matrix G is given by

Network homogenization occurs when the coefficient of variation of N is less than the coefficient of variation of G because this says that the network flow is more evenly distributed in the integral matrix. The test statistic employed here looks at whether or not the ratio CV(G)/ CV(N) exceeds 1. The interpretation again is clear that the view of flow in ecosystems is not as discrete as it appears because in fact the material is well mixed (i.e., homogenized) and has traveled through and continues to travel through many, if not, most parts of the system.

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