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112 evidence of models based on local rules by focusing on the distance between newly- linked users. Specifically, we examine the shortest path distance between the source and destination of newly created links, before a new link is created between them. If, for example, the BA model is the underlying mechanism, then the observed distance distribution between users should match that predicted by the model. Otherwise, if we see a stronger bias towards close users, it may suggest that users follow local, rather than global, rules for selecting the destinations for new links. Over 50% of the links in all five networks are between nodes that have, a priori, some network path between them (the remainder of the observed new links are be- tween users which are, a priori, disconnected).1 For these new links among already connected users, Figure 6.5 shows the cumulative distribution of shortest-path hop distances between source and destination nodes. It reveals a striking trend: over 80% of such new links in Flickr connect nodes that were only two hops apart, meaning that the destination node was a friend-of-a-friend of the source node. Similarly, this fraction is over 42% in YouTube-D, over 50% in Wikipedia, over 45% in YouTube-U, and over 57% in the Internet topology. One might wonder whether in small diameter networks like the ones we observe, this high level of proximity in link establishment is simply a result of preferential attachment. This is plausible, since the high-degree nodes that preferential attach- ment prefers tend to be close to many nodes. To test this hypothesis, for each newly 1For directed networks, we only count directed paths.PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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