  Complex networks have abundant and extensive applications in real life.
Recently, researchers have proposed a number of complex networks, in which some
are deterministic and others are random. Compared with deterministic networks,
random network is not only interesting and typical but also practical to
illustrate and study many real-world complex networks, especially for random
scale-free networks. Here, we introduce three types of operations, i.e., type-A
operation, type-B operation and type-C operation, for generating random
scale-free networks $N(p,q,r,t)$. On the basis of our operations, we put
forward the concrete process of producing networks, which constitute the
network space $\mathcal{N}(p,q,r,t)$, and then discuss their topological
properties. Firstly, we calculate the range of the average degree of each
member in our network space and discover that each member is a sparse network.
Secondly, we prove that each member in our space obeys the power-law
distribution with degree exponent $\gamma=1+\frac{\ln(4-r)}{\ln2}$, which
implies that each member is scale-free. Next, we analyze the diameter, and find
that the diameter may abruptly transform from small to large due to type-B
operation. Afterwards, we study the clustering coefficient of network and
discover that its value is only determined by type-C operation. Ultimately, we
make an elaborate conclusion. \\ \textbf{Keywords:} Random network; degree
distribution; diameter; clustering coefficient.
