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This paper discusses the asymptotic formula of average distances on node-weighted Sierpinski skeleton networks by using the integral of geodesic distance in terms of self-similar measure on the Sierpinski gasket with respect to the weight vector. [ABSTRACT FROM AUTHOR]

The substitution network is a deterministic model of evolving self-similar networks. For normalized substitution networks, the limit of metric spaces with respect to networks is a self-similar fractal and the limit of average distances on networks is the integral of geodesic distance of the fractal on the self-similar measure. After some technical handles, we establish the finiteness of integrals and obtain a linear equation set to solve the average distance on the fractal. [ABSTRACT FROM AUTHOR]

It is of great interest to analyze geodesics in fractals. We investigate the structure of geodesics in n -dimensional Sierpinski gasket F n for n ≥ 3 , and prove that there are at most eight geodesics between any pair of points in F n . Moreover, we obtain that there exists a unique geodesic for almost every pair of points in F n . [ABSTRACT FROM AUTHOR]

The eigentime identity for random walks on networks is the expected time for a walker going from a node to another node. In this paper, our purpose is to calculate the eigentime identities of flower networks by using the characteristic polynomials of normalized Laplacian and recurrent structure of Markov spectrum. [ABSTRACT FROM AUTHOR]

For a class of self-similar networks generated by substitution rules, we investigate them in terms of normalized Laplacian spectra. Accordingly, we obtain the recurrent structure of Markov spectra for these self-similar networks, and also estimate the smallest positive eigenvalue for Laplace operator. [ABSTRACT FROM AUTHOR]