  Social media outlets such as Twitter constitute valuable data sources for
understanding human activities in the virtual world from a geographic
perspective. This paper examines spatial distribution of tweets and densities
within cities. The cities refer to natural cities that are automatically
aggregated from a country's small street blocks, so called city blocks. We
adopted street blocks (rather than census tracts) as the basic geographic units
and topological center (rather than geometric center) in order to assess how
tweets and densities vary from the center to the peripheral border. We found
that, within a city from the center to the periphery, the tweets first increase
and then decrease, while the densities decrease in general. These increases and
decreases fluctuate dramatically, and differ significantly from those if census
tracts are used as the basic geographic units. We also found that the decrease
of densities from the center to the periphery is less significant, and even
disappears, if an arbitrarily defined city border is adopted. These findings
prove that natural cities and their topological centers are better than their
counterparts (conventionally defined cities and city centers) for geographic
research. Based on this study, we believe that tweet densities can be a good
surrogate of population densities. If this belief is proved to be true, social
media data could help solve the dispute surrounding exponential or power
function of urban population density.
  Keywords: Big data, natural cities, street blocks, urban density, topological
distance
