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93 for example, the overall average path length is 5.67, of which 3.5 hops involve the 10% of nodes in the core with the highest degrees. This suggests that the high-degree core nodes in these networks are all within roughly four hops of each other, while the rest of the nodes, which constitute the majority of the network, are at most a few hops away from the core nodes. 5 4 3 2 1 0.0001% 0.001% 0.01% 0.1% 1% 10% Fraction of Network Or kut LiveJourn al YouTube Flickr Figure 5.8 : Average path length among the most well-connected nodes. The path length increases sub-logarithmically. Thus, the graphs we study have a densely connected core comprising of between 1% and 10% of the highest degree nodes, such that removing this core completely disconnects the graph. The structure of social networks, with its high dependence on few highly connected nodes, may have implications for information flow, for trust relationships, and for the vulnerability of these networks to deliberate manipulation. The small diameter and path lengths of social networks are likely to impact the design of techniques for finding paths in such networks, for instance, to check how closely related a given pair of nodes Average Path LengthPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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