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37 The well-known Barab ́asi-Albert (BA) model [15], based on preferential attach- ment, has been shown to result in networks with power-law degree distributions. In the BA model, new links are attached to nodes using a probability distribution weighted by node degree, resulting in linear preferential attachment. Many extensions to the BA model have been proposed (e.g., to add a tunable level of clustering [67]). We are able to verify that the growth of online social networks follows linear prefer- ential attachment, but not in the way that the BA model proposes. Another class of models that produce power-law networks are based on local rules, such as the random walk model [142,154], where nodes select new neighbors by taking random walks; the common neighbors model [114], where nodes select new neighbors by picking nodes with whom they share many friends in common; and the finite memory model [79], where nodes eventually become inactive and stop receiving any new links. All of these models exhibit preferential attachment (since high-degree nodes end up being selected more often), but with higher levels of local clustering than the BA model [154]. We demonstrate that, while these models are more accurate at predicting the destination of new links in our data than the BA model, the overall accuracy of these models remains very low. For a more detailed treatment all of these models and others, we refer the reader to a paper by Mitzenmacher [106].PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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