  Using a geographical scale-free network to describe relations between people
in a city, we explain both superlinear and sublinear allometric scaling of
urban indicators that quantify activities or performances of the city. The
urban indicator $Y(N)$ of a city with the population size $N$ is analytically
calculated by summing up all individual activities produced by person-to-person
relationships. Our results show that the urban indicator scales superlinearly
with the population, namely, $Y(N)\propto N^{\beta}$ with $\beta>1$ if $Y(N)$
represents a creative productivity and the indicator scales sublinearly
($\beta<1$) if $Y(N)$ is related to the degree of infrastructure development.
These coincide with allometric scaling observed in real-world urban indicators.
We also show how the scaling exponent $\beta$ depends on the strength of the
geographical constraint in the network formation.
