Trantor

In Isaac Asimov's Foundation series, Trantor is the capital of the Galactic Empire, a planet-sized megacity of a hundred billion. But, according to Asimov, the Empire's excessive centralization around Trantor contributed to its fall:

To support the needs and whims of [Trantor's] population, food from twenty agriculturalships in the tens of thousands...[Trantor's] dependence upon the outer worlds for food and, indeed, for all necessities of life, made [the capital] increasingly vulnerable...In the last millennium of the Empire, the monotonously numerous revolts made Emperor after Emperor conscious of this, and Imperial policy became little more than the protection of Trantor's delicate jugular vein... worlds [was] brought by

Back in the real world, here's a story from China:

Emergency water started flowing to Beijing Thursday as a six-month scheme kicked off to keep the city of 17 million from running out of the resource, the government said.

Some 300 million cubic metres (10.6 billion cubic feet) of water will be redirected from Hebei province, which surrounds the capital, the state's government said.

Hebei also suffers severely from a lack of water, and the fact that it must pass on the scarce resource is testimony to Beijing's political clout, experts say...

"The transfer of emergency water to the capital Beijing is a politically important issue of major significance to the economy of our province," the statement said.

Luckily, China's psychohistorians are hard at work protecting their civilization's future from any possible threat...