Following a post on the verification of Zipf's law for cities in Iran, here I am testing whether the Zipf's law also holds true in Australia where the growth of cities has not been completely natural with many historical and political changes, mainly immigration.
This is a chart showing the Australian significant urban areas ranked by population. Melbourne and Sydney's population are very close which contradicts the Zipf's law that the second city in the ranking list should have half population of the first city. This might be due the man-forced changes happened throughout the years in Australia and the immigration policies.
However, if we look at the rest of the cities, they closely follow the Zipf's law. The following figure shows the log population versus log ranking of cities in Australia. Excluding Sydney from the analysis, Melbourne, Brisbane, Perth, and other cities line up nicely for a power law to fit. Of course, further investigation is needed to better understand the population growth patterns in Australia.