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 Barabási-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 Barabási-Albert scale-free networks, four synthetic Watts-Strogatz small-world networks, and on a real email network with known degree distributions.