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Impact of degree heterogeneity on the behavior of trapping in Koch networks
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Image of FIG. 1.
FIG. 1.

Iterative construction method for the Koch networks.

Image of FIG. 2.
FIG. 2.

A network corresponding to the case of .

Image of FIG. 3.
FIG. 3.

Labels of all nodes in .

Image of FIG. 4.
FIG. 4.

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 .

Image of FIG. 5.
FIG. 5.

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.

Image of FIG. 6.
FIG. 6.

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).


Generic image for table
Table I.

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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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Impact of degree heterogeneity on the behavior of trapping in Koch networks