  It is well-known that the scale-free networks are ubiquitous in nature and
society and have been one of the hotspot topic in complex networks. Recently,
scholars presented a large quantity of scale-free networks by calculating
cumulative distribution. The purpose of this paper is to discuss the
relationship between two cumulative distributions, namely, cumulative
distribution, edge-cumulative distribution. Here, firstly, we introduce a
relationship between degree distribution and cumulative distribution. Secondly,
we introduce the definition of cumulative distribution and edge-cumulative
distribution, and compare the relationship between them. Thirdly, we apply
algorithmic techniques to construct three deterministic networks, calculate
their cumulative distribution and edge-cumulative distribution, and analyze the
relationship between cumulative distribution and edge-cumulative distribution.
Finally, we offer some open problems for future research in order to understand
the interplay between the degree distribution, cumulative distribution and
edge-cumulative distribution.
