  Over the last decades, in disciplines as diverse as economics, geography, and
complex systems, a perspective has arisen proposing that many properties of
cities are quantitatively predictable due to agglomeration or scaling effects.
Using new harmonized definitions for functional urban areas, we examine to what
extent these ideas apply to European cities. We show that while most large
urban systems in Western Europe (France, Germany, Italy, Spain, UK)
approximately agree with theoretical expectations, the small number of cities
in each nation and their natural variability preclude drawing strong
conclusions. We demonstrate how this problem can be overcome so that cities
from different urban systems can be pooled together to construct larger
datasets. This leads to a simple statistical procedure to identify urban
scaling relations, which then clearly emerge as a property of European cities.
We compare the predictions of urban scaling to Zipf's law for the size
distribution of cities and show that while the former holds well the latter is
a poor descriptor of European cities. We conclude with scenarios for the size
and properties of future pan-European megacities and their implications for the
economic productivity, technological sophistication and regional inequalities
of an integrated European urban system.
