Barabási & Albert (1999) showed that many real-world networks — the web, citation networks, actor collaborations — aren't wired randomly. They grow over time, and new nodes preferentially attach to nodes that are already well-connected ("the rich get richer"). These two simple ingredients are enough to produce scale-free networks: a few highly-connected hubs and a power-law degree distribution P(k) ~ k-3 — a straight line on a log-log plot — with no hub deliberately designed.
Grow the network below under preferential attachment and watch hubs emerge, then switch to random attachment (growth alone, no preference for popular nodes) and see the degree distribution curve away from a straight line instead.