⁴This example is only illustrative. Of course, if we increased the total in-flows, this would imply that we are also increasing the total out-flows from somewhere else and therefore the system could not truly be held constant. However, substantive modeling calls for origin and destination variables that are not derived from the interaction matrix. Therefore, this is not an issue in practice when there is the assumption of independence between flows. It should also be noted that it has been hypothesized that flows may not be independent and therefore more accurate estimates can be obtained using more advanced methods (LeSage, Pace 2008, Chun 2008).