  In many networks of scientific interest we know that the link between any
pair of vertices conforms to a specific probability, such as the link
probability in the Barab\'asi-Albert scale-free networks. Here we demonstrate
how the distributions of link probabilities can be utilized to generate various
complex networks simply and effectively. We focus in particular on the problem
of complex network generation and develop a straightforward paradigm by using
the strategy of vertex selecting-and-pairing to create complex networks more
generic than other relevant approaches. Crucially, our paradigm is capable of
generating various complex networks with varied degree distributions by using
different probabilities for selecting vertices, while in contrast other
relevant approaches can only be used to generate a specific type of complex
networks. We demonstrate our paradigm on four synthetic Barab\'asi-Albert
scale-free networks, four synthetic Watts-Strogatz small-world networks, and on
a real email network with known degree distributions.
