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Access to facilities, services and socio-economic opportunities plays a critical role in the growth and decline of cities and human settlements. Previous attempts to explain changes in socio-economic indicators by differences in accessibility have not been convincing as countries with highly developed transport infrastructure have only seen marginal benefits of infrastructure improvements. Australia offers an ideal case for investigating the effects of accessibility on development since it is seen as home to some of the most liveable cities in the world while, at the same time, it also has some of the most isolated settlements. We investigate herein the connectivity and accessibility of all 1814 human settlements (population centers exceeding 200 persons) in Australia, and how they relate to the socio-economic characteristics of, and opportunities in, each population center. Assuming population as a proxy indicator of available opportunities, we present a simple ranking metric for a settlement using the number of population and the distance required to access all other settlements (and the corresponding opportunities therein). We find a strikingly unequal distribution of access to opportunities in Australia, with a marked prominence of opportunities in capital cities in four of the eight states. The two largest cities of Sydney and Melbourne have a dominant position across all socio-economic indicators, compared to all the other cities. In general, we observe across all the settlements that a decrease in access to opportunities is associated with relatively greater socio-economic disadvantage including increased median age and unemployment rate and decreased median household income. Our methodology can be used to better understand the potential benefits of improved accessibility based on infrastructure development, especially for remote areas and for cities and towns with many socio-economically disadvantaged population. [ABSTRACT FROM AUTHOR]