  Faced with the ever-increasing trend of the cellular network scale, how to
quantitatively evaluate the effectiveness of the large-scale deployment of base
stations (BSs) has become a challenging topic. To this end, a deeper
understanding of the cellular network topology is of fundamental significance
to be achieved. In this paper, $ \alpha $-Shape, a powerful algebraic geometric
tool, is integrated into the analysis of real BS location data for six Asian
countries and six European countries, respectively. Firstly, the BS spatial
deployments of both Asian and European countries express fractal features based
on two different testifying metrics, namely the Betti numbers and the Hurst
coefficients. Secondly, it is found out that the log-normal distribution
presents the best match to the cellular network topology when the practical BS
deployment is characterized by the Euler characteristics.
