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Optimal Data Collection For Informative Rankings Expose Well-Connected Graphs

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Figure

Table 1: A comparison of several measures of connectivity for 4 well-known graphs. Weassume n ≥ 3
Figure 1: The 4- and 5-node connected graphs and their algebraic connectivity, λ2. Graphswith large algebraic connectivity represent data sets with informative rankings.See Section 5.1.
Figure 2: Targeted data collection for small graphs. (left) The five topologically distinctconnected graphs with n = 5 nodes and m = 6 edges
Figure 3: Algebraic connectivity, λ2 as a function of m for 50- and 100-node graphs. Thedashed blue line represents the upper bound on λ2 given in (7)
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