Methods And Problems Attempt in Scale-Free Models From Complex Networks

Abstract

Abstract. The dynamical phenomena of complex networks are not easy to model and to characterize by current methods of mathematics. Newman, Barabási and Watts pointed out the direction of researching complex networks by graph theory, which was successfully applied in current investigation of complex networks, and Newman's network-based methods have been applied to a variety of fields. Some well-known and new methods of mathematics are provided in this article, associated with construction and problems on scale-free models from real networks.

The Characteristics of Compound Models Designed for Internet of Things

“…However, we can not say that the second compound model G (2) (t) to be spares, since it is not easy to show the main average degree…”

“…(2) is the result of a fractal 2-operation. (2) (t) (see Fig.8 and Fig.9). For computation of degree spectrums of two compound models G (1) (t) and G (2) (t) at time step t, let n v (s) (t) and n e (s) (t) be the numbers of vertices and edges of G (2) and moreover…”

“…for large t. For dealing with various parameters of G (2) (t), we have to consider the values of two numbers X (2) and Y (2) , where…”

“…Two fractal 2-operations are shown in Fig.6 and Fig.7 (Ref. [1], [2], [3], [9]). Three Sierpinski models S(0), S (1) and S (2) are shown in Fig.5, and furthermore S(1) and S (2) are constructed by the fractal 2-operation.…”

“…[1], [2], [3], [9]). Three Sierpinski models S(0), S (1) and S (2) are shown in Fig.5, and furthermore S(1) and S (2) are constructed by the fractal 2-operation. Especially, ``joining a vertex (or generator) with another vertex (or generator) by an edge'' is regarded as a 2-operator on them, especially, write this 2-operator by Oo, and the 2-operator set O contains it in any time.…”