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Dense graphs with scale-free feature | | Fei Ma
; Xiaomin Wang
; Ping Wang
; Xudong Luo
; | | Date: |
2 Dec 2019 | | Abstract: | Complex networks, representing various of complex systems, have attracted
more attention from a broad range of science fields in recent years. The both
prominent characters, scale-free feature and small-world property, have been
extensively observed in a large amount of complex networks. While the authors
in Ref cite{C-I-D-G-2011} had already stated that all scale-free networks are
sparse, there exist some real-world networks, for instance, social networks
cite{Leskovec-2007}, urban networks cite{Schlapfer-2014}, information
networks cite{Lambiotte-2016}, which are by observation dense. To understand
both dynamics and structure on these such networks, recently much effort has
been spent and hence many techniques have developed. By contrast, in this
paper, we propose a novel framework for generating scale-free graphs with dense
feature using two simple yet helpful operations, first-order subdivision and
Line-operation, from graph theory. It turns out both analytically and
numerically that our instrument is more convenient to implement than those
pre-existing methods. From theoretical point of view, our method can be used
not only to produce desired scale-free graphs with power-law exponent $1<
gammaleq2$ but also to establish unexpected networked models which disprove
some widely known statements, such as "Scale-free networks are ultrasmall" due
to Cohen, emph{et al}, in cite{R-C-2003}. Our findings may shed lights on the
fundamental understanding of complex networks, in particular, scale-free
graphs. | | Source: | arXiv, 1912.8923 | | Services: | Forum | Review | PDF | Favorites | |
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