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92 As we remove the highest degree nodes, the largest SCC begins to split into smaller-sized SCCs. Figure 5.7 shows the composition of the splits as we remove between 0.01% and 10% of the highest-degree nodes in Flickr. The corresponding graphs for the other social networks look similar, and we omit them for clarity. Once we remove 10% of the highest indegree nodes,5 the largest SCC partitions into millions of very small SCCs consisting of only a handful of nodes. 1 0.8 0.6 0.4 0.2 0 Large SCC 8-63 Nodes 2-7 Nodes 1 Node 0.01% 0.1% 1% 10% Fraction of Network Removed Figure 5.7 : Breakdown of network into SCCs when high-degree nodes are removed, grouped by SCC size. To understand how much the network core contributes towards the small path lengths, we analyzed the path lengths of subgraphs containing only the highest-degree nodes. Figure 5.8 shows how path lengths increase as we generate larger subgraphs of the core by progressively including nodes ordered inversely by their degree. The average path length increases sub-logarithmically with the size of the core. In Flickr, 5We obtained the similar results when using both indegree and outdegree, thus we only present the indegree results here. Sizes of SCCsPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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