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I came across the following derivation from a paper "Pfeiffer III, Joseph J., et al. "Fast generation of large scale social networks with clustering." arXiv preprint arXiv:1202.4805 (2012)."

In the attached equation,

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I am not able to understand how they got rid of $D_k^2$ in the numerator and the denominator from line 3 to 4. Although the final results hold even while using $D_k^2$, I am unable to understand if this is just a typo or some reduction step that I did not understand.

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Seems like a typo, but it has no effect on the final conclusion since $$ \frac{\sum_{k}D_{j}D_{k}^{2}D_{i}\frac{1}{D_{j}^{CL}D_{k}^{CL}}}{\sum_{i^{\prime}}\sum_{k}D_{j}D_{k}^{2}D_{i^{\prime}}\frac{1}{D_{j}^{CL}D_{k}^{CL}}}=\frac{D_{i}\left(\sum_{k}D_{k}^{2}\frac{1}{D_{k}^{CL}}\right)}{\left(\sum_{i^{\prime}}D_{i^{\prime}}\right)\left(\sum_{k}D_{k}^{2}\frac{1}{D_{k}^{CL}}\right)}=\frac{D_{i}}{\sum_{i^{\prime}}D_{i^{\prime}}}. $$

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  • $\begingroup$ thanks for confirmation. $\endgroup$ – learner Dec 19 '17 at 5:06

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