Final answer:
The Danube River is the river that flows through the center of Hungary and Budapest. It is a key transportation route that passes through several European cities and empties into the Black Sea.
Step-by-step explanation:
The river that flows through the center of Hungary, including its capital Budapest, is the Danube River. This south-flowing river is integral to the region and has historically been a significant waterway for transport and trade.
In addition to Budapest, the Danube passes through other major European cities, such as Vienna and Belgrade, before eventually emptying into the Black Sea. The river has not only shaped the cultural and economic landscape of Hungary but has also served as a crucial natural resource and mode of transportation throughout Eastern Europe.
Furthermore, the Danube River is connected to a network of other important European rivers and canals. It connects to the Main River, which then flows into the Rhein River in Germany, forming a major waterway system that has been used historically for shipping and trade and continues to have significant economic and geopolitical relevance today.