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Proof. For a matrix M and subsets X, Y of indices of rows and columns, we denote a submatrix Mx,Y of M by restricting rows and columns of M to X and Y. We consider the determinant of £(3 as follows: det £fj = det SfTWfjS' = L (det Sp,v)( det WF,F)(det Sp,v) FCVUE IFI=n 52 F. Chung and W. Zhao by the Cauchy-Binet Theorem. We note that det S~,v = 0 if F contains a cycle. In the other direction, if F does not contain a cycle, F is a spanning forest and the vertices in F n V are the k roots of the spanning forest.
Edu BOLVAI SOCIETY MATHEMATICAL STUDIES, 20 Fete of Combinatorics, pp . 43-62 . PAGERANK AND RANDOM WALKS ON GRAPHS FAN CHUNG and WENBO ZHAO Dedicated to Loiuisz on the ocassion of his sixtieth birthday We examine the relationship between PageRank and several invariants occurring in the study of random walks and electrical networks . We consider a generalized version of hitting tim e and effective resistance with an additional parameter which controls the 'speed' of diffusion. We will establish their connection with PageRank.
Viola Meszaros was also partially supported by OTKA Grant K76099. Josef Cibulka and Rudolf Stolar were also supported by the Czech Science Foundation under the contract no. 201/09/H057. t A short version of the paper appeared in Combinatorial Algorithms, the proceedings of the IWOCA 2009, Hradec nad Moravici, Czech Republic , LNCS, Vol. 5874, pp . 356-368 , Springer (2009) . 64 J. Cibulka, J. Kync], V. Meszaros , R. Stolar and P. Valtr of not necessarily equal size. Afterwards they take turns alternately to divide it among themselves.