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6.3 Reciprocation We begin by first examining reciprocation, a growth mechanism that exists only in directed graphs. Reciprocation occurs when the creation of a directed link between two nodes causes the reverse link be established. Since undirected graphs are, by definition, symmetric, reciprocation does not make sense in the context of undirected graphs. Reciprocation has been proposed as an independent growth mechanism for large-scale directed graphs [56,173]. Since we do not know why links were established, we rely on the timing between the creation of the two directed links of a symmetric link to guess whether the creation of the first causally affected the second. Figure 6.1 shows the distribution of the time between the establishment of the two links of a given symmetric link in the three directed graphs (Flickr, YouTube-D, and Wikipedia) that we studied. 1 0.8 0.6 0.4 0.2 0 Time Between Establishment of Two Halves of Link (days) Figure 6.1 : CDF of time between establishment of the two directed links of a sym- metric link. In both Flickr and Youtube, links are quickly reciprocated. From Figure 6.1, it is clear that in the two social networks we observed, users 106 Flickr YouTube-D Wikipedia 0 5 10 15 20 25 30 CDFPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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