Random walks on Fibonacci treelike models: emergence of power law
Abstract
In this paper, we propose a class of growth models, named Fibonacci trees $F(t)$, with respect to the intrinsic advantage of Fibonacci sequence $\{F_{t}\}$. First, we turn out model $F(t)$ to have powerlaw degree distribution with exponent $\gamma$ greater than $3$. And then, we study analytically two significant indices correlated to random walks on networks, namely, both the optimal mean firstpassage time ($OMFPT$) and the mean firstpassage time ($MFPT$). We obtain a closedform expression of $OMFPT$ using algorithm 1. Meanwhile, algorithm 2 and algorithm 3 are introduced, respectively, to capture a valid solution to $MFPT$. We demonstrate that our algorithms are able to be widely applied to many network models with selfsimilar structure to derive desired solution to $OMFPT$ or $MFPT$. Especially, we capture a nontrivial result that the $MFPT$ reported by algorithm 3 is no longer correlated linearly with the order of model $F(t)$.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.11314
 Bibcode:
 2019arXiv190411314M
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks