Author(s)

Levente Simon^1,2, Anna Soós^1*

¹Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania.
²Faculty of Informatics, Eötvös Loránd University, Budapest, Hungary.

We propose a new approach to the investigation of deterministic self-similar networks by using contractive iterated multifunction systems (briefly IMSs). Our paper focuses on the generalized version of two graph models introduced by Barabási, Ravasz and Vicsek ([1] [2]). We generalize the graph models using stars and cliques: both algorithm construct graph sequences such that the next iteration is always based on n replicas of the current iteration, where n is the size of the initial graph structure, being a star or a clique. We analyze these self-similar graph sequences using IMSs in function of the size of the initial star and clique, respectively. Our research uses the Cantor set for the description of the fixed set of these IMSs, which we interpret as the limit object of the analyzed self-similar networks.

Cantor Set, Fixed Set, Iterated Function Systems, Iterated Multifunction Systems, Self-Similar Graphs

Simon, L. and Soós, A. (2016) Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks. Applied Mathematics, 7, 365-374. doi: 10.4236/am.2016.74034.