It's a very nice paper. There are some parts I don't fully understand yet, as I have to read more on hyperLoglog counter and webgraph framework. ### Comparison to existing methods: Doing some experimental comparisons to [Eppstein and Wang 2004]( for the closeness centrality might be interesting. ### Typos: - $\mathscr{B}_{G}(x,r)=\{y | d(x,y) \leq r\}$ instead of $\mathscr{B}_{G}(x,r)=\{y | d(x,y) \leq t\}$ - $|\mathscr{B}_{G}(v,t)|-|\mathscr{B}_{G}(v,t-1)|$ instead of $|\mathscr{B}_{G}(v,t+1)|-|\mathscr{B}_{G}(v,t)|$. This is corrected in the other formula on centralities. - "the the reciprocal of a" - "can be easily computed in a cumulative fashion nothing that" - "on the approximation the diameter" - "its importance it by 1/2" ### Minors: - "Nodes with empty coreachable set have centrality 1 by definition" . By definition the coreachable set of a node is never empty, it contains at least the concerned node.

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