English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We constructed the random SA-mixed models based on Sierpinski and 2-dimension Apollonian networks having scale-free properties, and we have shown our random SA-mixed models are scale-free. It is noticeable, adding unchanged motifs doesn't affect the scale-free behaviors of the origin networks. The random SA-mixed models are scale-free by proofs of extremum methods. Introduction Many real-life networks can be described as scale-free network models. In recent years, with the rapid development of the Internet of Things [1][2], it shows the scale-free feature increasingly in metabolic networks, communication networks and scientific literature [3][4]. In order to explore the topological structures of real-world networks, the researchers have built a variety of scale-free models. Such as deterministic scale-free web and deterministic recursive graphs, Sierpinski networks [5] and Apollonian networks [6] etc. Network motifs are an important local property of networks, and have been identified in a wide range of networks across many scientific disciplines and are suggested to the basic building blocks of most complex networks [7][8]. Motifs are of notable importance largely because they may reflect functional properties, and they have recently gathered much attention as a useful concept to answer structural design principles of scale-free networks, and may provide a deep insight into the network's functional abilities [9]. In this paper, we, in order to mimic real-world networks, build up SA-mixed models on the basis of Sierpinski networks and 2-dimension Apollonian networks by using the idea of motifs. We add motifs randomly in the SA-mixed models, therefore, it can simulate real networks better, and verify its scale-free by proving the scale-freeness of maximal model and minimal model respectively to approximate it. In addition, we prove the scale-freeness、the velocities of Sierpinski networks, Apollonian networks and SA-mixed models. Our results show that the velocity of SA-mixed models is faster than other two networks. It is a guidance for us to build different networks according to the needs of human. SA-mixed models We define some fractal operations before we show our models, and some fractal operations can be found in [5]. Let S(0) be a graph having three vertices A,B,C and three edges such that any pair of vertices is joined by an edge, we call S(0) a triangle (see Figure 1(a) and (b)). Clearly, the triangle S(0) divides the plane into two parts: One is out of S(0), called the outer face of S(0); one is inside S(0), called the inner face of S(0). A fractal (1)-operation yields a configuration H(1) (see Figure 1(c)) in the way: Add a vertex u into the inner face of a triangle shown in Figure 1(a), and then join u with three vertices A, B and C by three edges, respectively. We define a labelling function g for H(1) as: g(A)=g(B)=g(C)=k-1, 6th International Conference on Machinery, Materials, Environment, Biotechnology and Computer (MMEBC 2016) © 2016. The authors Published by Atlantis Press 1875

On Random SA-mixed Network Models Generated From Sierpinski and Apollonian networks