### Question Involving Equation 6

#### Posted by dmack on 07 Mar 2011 at 09:31 GMT

I find the application of this paper very entertaining, and the derived prestige scoring equation interesting. My question is in the authors description of how equation 6 is solved when q = 0. The solution appears to be undefined as both the numerator and denominator both are 0. I examined the limit as q approaches 0 and still found a different analytical form. Would if be possible for the authors to clarify the steps between Eq 6 and Eq 7?

One further question, I assume the authors showed this analytical form for the single tournament, but then used the earlier "algorithm" with the whole form of the prestige score for the graphs they created? It was unclear, as the paper seemed to be building using the straight analytical form for the single tournament.

No competing interests declared.

### RE: Question Involving Equation 6

#### filrad replied to dmack on 10 Mar 2011 at 06:14 GMT

In both cases, we need to calculate the sum
\sum_{i=0}^{\ell-1} [(2-q)/2]^i. If q>0, then (2-q)/2<1 and we can apply the steps described in the paper to arrive to Eq.6. Conversely, if q=0 then (2-q)/2=1 and the sum reduces to \sum_{i=0}^{\ell-1} 1 = \ell. This leads to Eq.7.
Alternatively, we can obtain Eq.7 directly from Eq.6. Take the limit q to 0 in Eq.6 and apply the L'Hôpital's rule.

Eqs. 6 and 7 are the solutions of the PageRank equation (Eq.1) in the case of a single tournament. These equations are not used for the generation of the tables reported in the paper. These table are based on the numerical solution of Eq.1 .

Competing interests declared: I am the author of the paper.