  Complex networks have recently aroused a lot of interest. However, network
edges are considered to be the same in almost all these studies. In this paper,
we present a simple classification method, which divides the edges of
undirected, unweighted networks into two types: p2c and p2p. The p2c edge
represents a hierarchical relationship between two nodes, while the p2p edge
represents an equal relationship between two nodes. It is surprising and
unexpected that for many real-world networks from a wide variety of domains
(including computer science, transportation, biology, engineering and social
science etc), the p2c degree distribution follows a power law more strictly
than the total degree distribution, while the p2p degree distribution follows
the Weibull distribution very well. Thus, the total degree distribution can be
seen as a mixture of power-law and Weibull distributions. More surprisingly, it
is found that in many cases, the total degree distribution can be better
described by the Weibull distribution, rather than a power law as previously
suggested. By comparing two topology models, we think that the origin of the
Weibull distribution in complex networks might be a mixture of both
preferential and random attachments when networks evolve.
