Iterative construction method for the Koch networks.
A network corresponding to the case of .
Labels of all nodes in .
Growth of first-passage time in going from to in the case of . Node has neighbor nodes in generation (○) and new neighbor nodes in generation (◻). A new neighbor of node has a degree of 2, and is simultaneously linked to another new neighbor of .
Illustration showing the relation of the first-passage times for each pair of two new nodes ( and with , or ) and the old node as one point of the triangle generating the new nodes.
Mean first-passage time as a function of the generation on a semilogarithmic scale for different values of . The empty symbols represent the numerical results obtained by direct calculation from Eq. (20), while the filled symbols correspond to the rigorous values provided by Eq. (18).
First-passage time for a random walker starting from node in for different . Note that, thanks to the symmetry, nodes in the same column are equivalent to one another, since they have the same FPT.
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