Cantor Type Fixed Sets of Iterated Multifunction Systems Corresponding to Self-Similar Networks  

作　　者：Levente Simon Anna Soós Levente Simon;Anna Soós(Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania;Faculty of Informatics, Eötvös Loránd University, Budapest, Hungary)

机构地区：[1]Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania [2]Faculty of Informatics, Eö tvö s Loránd University, Budapest, Hungary

出　　处：《Applied Mathematics》2016年第4期365-374,共10页应用数学（英文）

摘　　要：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.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.

关 键 词：Cantor Set Fixed Set Iterated Function Systems Iterated Multifunction Systems Self-Similar Graphs 

分 类 号：O15[理学—数学]