A class of vertex–edge-growth small-world network models having scale-free, self-similar and hierarchical characters

Fei Ma, Jing Su, Yongxing Hao, Bing Yao and Guanghui Yan

Physica A: Statistical Mechanics and its Applications, 2018, vol. 492, issue C, 1194-1205

Abstract: The problem of uncovering the internal operating function of network models is intriguing, demanded and attractive in researches of complex networks. Notice that, in the past two decades, a great number of artificial models are built to try to answer the above mentioned task. Based on the different growth ways, these previous models can be divided into two categories, one type, possessing the preferential attachment, follows a power-law P(k)∼k−γ, 2<γ<3. The other has exponential-scaling feature, P(k)∼α−k. However, there are no models containing above two kinds of growth ways to be presented, even the study of interconnection between these two growth manners in the same model is lacking. Hence, in this paper, we construct a class of planar and self-similar graphs motivated from a new attachment way, vertex–edge-growth network-operation, more precisely, the couple of both them. We report that this model is sparse, small world and hierarchical. And then, not only is scale-free feature in our model, but also lies the degree parameter γ(≈3.242) out the typical range. Note that, we suggest that the coexistence of multiple vertex growth ways will have a prominent effect on the power-law parameter γ, and the preferential attachment plays a dominate role on the development of networks over time. At the end of this paper, we obtain an exact analytical expression for the total number of spanning trees of models and also capture spanning trees entropy which we have compared with those of their corresponding component elements.

Keywords: Network models; Vertex–edge-growth operation; Scale-free feature; Small-world property; Spanning trees (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437117311366
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:492:y:2018:i:c:p:1194-1205

DOI: 10.1016/j.physa.2017.11.047

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().