A small-world and scale-free network generated by Sierpinski Pentagon

Abstract

The Sierpinski Pentagon is used to construct evolving networks, whose nodes are all solid regular pentagons in the construction of the Sierpinski Pentagon up to the stage t and any two nodes are neighbors if and only if the intersection of corresponding pentagons is non-empty and non-singleton. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.

Hitting time for random walks on the Sierpinski network and the half Sierpinski network

“…In the same way, we now let (i 2 , j 2 , k 2 ) denote the three vertices of a lacunary region of size 2 in the network, such as (7,9,22) or (35,37,63); (I 2 , J 2 , K 2 ) label the three vertices of the triangle containing (i 2 , j 2 , k 2 ) as its central lacunary region, such as (1,20,24) or (20,61,65). It then follows the scaling derived previously that is as follows: Frontiers in Physics frontiersin.org…”