The bulb ( rhizome ) is what the plant grows from. It is a large white mass right beneath the soil where the new leaves come from. When winter comes, the plant will die back to that part. That is the heart of the plant.
Sort of like a tulip. But not quite.
When you see smaller plants around the larger one, they are not connected by root. You can pull them away. Just be very careful about it.
You are welcome for your plant and info. That is what I am here for