The community is a broad generalization as the fact, that when push comes to shove, everyone identifies with those most similar to them. Blacks will always identify moreso with other blacks and whites with whites, etc etc. Not to say that in every day life, in normal people there is this massive division, but its instinctual to congregate around those similar to you.
Then consider social standing, are you lower, middle, or upper class. Because you are able to afford 'x' you usually live in a certain area. That makes you more "related" to those in that area, ie you'll identify with folks in that area. Social standing can transcend heritage, and sadly, for many it does. Upper class will have a hard time socializing with lower class for longer periods. They'll enjoy different things or in different ways. Unless that upper class person comes from lower class, and remains humble, they most likely won't ever go to "that level" so associate.
So assume you have an Asian middle class person. They will associate with other Asians in the middle class, if available. If there are no Asians in their area in the middle class, they will more than likely seek out the "Asian community" to maintain their heritage. Like in my town, there is a small Japanese community. The folks all get together and spend time, but all are middle or upper class. Assuming a lower class Japanese person, they too would be included. But when they go home to their own neighborhoods, the upper class will be part of the upper class community and the lower class a part of the lower class community.
"Community" is transcendable or transferable at the individual level, but they do in fact exist. Individuals are considered "representatives" of the community to which they can be identified by the masses or in generalizations. I am a foreigner in Japan, I am a "representative" of the USA, even though I don't work for the government and am not here for international relations. BUT, because I am the only American many Japanese will interact with, they will form their opinion of Americans and America on me. I had one of my Japanese students go to Disney World for her honeymoon. She came back in shock (still enjoyed herself), because America is nothing like what I had been portraying while in Japan - not everyone is a gentleman, caring, and willing to go out of their way to help - her words, not mine.
So as much as it sucks, black people are representatives of the black community as much as I am a representative of the white community. And only in generalizations is this brought up. On the individual level you are just a person, but there are greater dynamics involved.