[Minato Ku]

Rhine-Ruhr is an area of several cities close to each other that grew independently of each other.
There isn't a core that dominate because it never was a single city that fueled the growth of a region. It's not a single market.
People don't settle to Duisbourg to work in Essen or Düsseldorf. It's not a single market area. I would say it's not a city but several cities close to each other.

The result is that despite a 11 million inhabitants population, the regional Rhine-Ruhr. S-bahn only carries something like 130 million passengers annual passengers.
That's less than the S bahn of Munich or Frankfurt despite being in less populated region.
People don't commute that far and don't need to use the S-Bahn.

To put thing in perspective, Paris RER/suburban network has a ridership 10 times higher than Rhine-Ruhr S-Bahn.

We have to ask a question, what is a city and what is a metropolitan area? This question is even more important in very dense region or countries where cities can be very close to each other or even touching each and yet still working independently.
I would never say that Rhine-Ruhr is a bigger city than Madrid because I don't considere Rhine-Ruhr to be a single city.

I would say the same about Randstad in Netherlands or Pearl River Delta in China.
Even Philalephia and New York City. Those are clearly two separate cities and two separate markets even if the sprawl means that their urban areas are merging.