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Existence is a social construction, too.
By this logic, no social groups exist by label. If a group of people declares, "we are a gang," is it somehow different than saying, for example, "we are a math club," "we are an acting troupe," or, "we are the Church of the Flying Spaghetti Monster?"
Any idea "exists," even if it only exists as a series of electrical impulses in one person's brain. If someone forms the idea of a gang, then that idea exists.
Youths form lots of friendship groups and these groups are stronger or weaker than other bonds. They only are considered 'gangs' by the state as a means to label and deal
I suppose much of our perception and imagination of gangs has been strongly influenced by sensationalist media
What is your definition of a "gang". A friendship group with a common interest in high school is marginally different from a rebellious, potentially violent group of youths who seek violence in their environment.