The perilous state of the eurozone economy will be an early test for Christine Lagarde when she succeeds Mario Draghi as president of the European Central Bank in October. Mr. Draghi is expected to announce a new package of stimulus measures next month, but Ms. Lagarde will have to consider what the central bank can do if the situation gets worse.

When Germany’s official statistics office reported on Wednesday that the economy shrank 0.1 percent in the second quarter, shock waves rippled through stock markets around the world. The reaction reflected the degree to which Germany sets the tone for the Continent.

Germany has the eurozone’s biggest economy, accounting for more than a quarter of the bloc’s output. It has the most people, 83 million, and the most workers, who help stoke nearly every other country’s economy. The list of European Union countries that count Germany as their No. 1 trading partner is long. It includes France, Italy, the Netherlands, Belgium, Slovakia and Sweden.

The relationships sometimes border on dependency. Germany accounts for 27 percent of Poland’s foreign trade. Britain, Poland’s No. 2 trading partner, accounts for only 6 percent, according to World Bank data.

Suppliers throughout Europe earn much of their revenue by selling to big German manufacturers like Daimler, Siemens and ThyssenKrupp. But those companies are struggling.

Daimler, the maker of Mercedes-Benz cars, has issued three profit warnings since October. Siemens, whose products include high-speed trains and equipment for oil and gas producers, this month reported a 6 percent decline in net profit. And the ratings firm Moody’s downgraded ThyssenKrupp’s debt further into junk territory this week, an indication that the giant steel maker is considered a default risk.

As it strains against the German downdraft, Europe is battling a host of other woes. High on the list is Italy, which has a stagnant economy, an unstable government and one of the highest debt burdens in the world, giving it the potential to touch off another financial crisis.