whatTwo networks grow side by side from the same stream of newcomers, each arrival bringing two links. On the left, a newcomer attaches to existing nodes in proportion to their degree: the well-connected are easier to find, so the rich get richer. On the right, the same arrivals attach uniformly at random. Every node is drawn at the size of its degree; under each network is its own log-log survival plot of who has how many links.

whyThe claim, from Barabasi and Albert: that one-word difference grows HUBS. The favouritism network sprouts a few swelling centres that hoover up links from every cohort, and its survival plot falls on a straight line, the scale-free signature behind the web, citations, and airline maps: hubs three to five times anything the uniform twin ever grows, tail slope near minus two. The no-favourites twin, fed exactly the same newcomers, stays an even mesh with an exponentially sagging tail.

howThe Barabasi-Albert urn: every edge endpoint goes into a bag, and a proportional-to-degree choice is one uniform draw from the bag. Both networks replay the same seeded arrival stream, so the twins differ only in the attachment rule. Grown to three hundred sixty nodes, held, then rescattered to grow again; click to rescatter now. One integer seeds every arrival and every choice.