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87 networks. Figure 5.5 plots the cumulative distributions of the outdegree-to-indegree ratio for the four social networks and the Web. The social networks show a remarkable correspondence between indegree and outdegree; for all networks, over 50% of nodes have an indegree within 20% of their outdegree. The distribution for the Web is markedly different; most nodes have considerably higher outdegree than indegree, while a small fraction of nodes have significantly higher indegree than outdegree. The high correlation between indegree and outdegree in social networks can be explained by the high number of symmetric links. The high symmetry may be due to the tendency of users to reciprocate links from other users who point to them. This process would result in active users (who place many outgoing links) automatically receiving many incoming links, and lead to the distributions we have observed. 5.5 Path lengths and diameter Next, we look at the properties of shortest paths between users. Table 5.3 shows the average path lengths, diameters, and radii3 for the four social networks. In absolute terms, the path lengths and diameters for all four social networks are remarkably short. Interestingly, despite being comparable in size to the Web graph we considered, the social networks have significantly shorter average path lengths and diameters. This property may again result from the high degree of reciprocity within the social 3Due to the computational complexity associated with determining the actual radius and diam- eter, the numbers presented here are from determining the eccentricity of 10,000 random nodes in each network.PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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