An efficient method of generating deterministic small-world and scale-free graphs for simulating real-world networks

We propose a novel mechanism to generate a family of deterministic small-world and scale-free networks by inserting new nodes into old nodes. These models can characterize the distinguishing properties of many real-world networks because this novel class of networks incorporates some key properties characterizing a majority of real-world networked systems, namely a high clustering coefficient and a short characteristic path length. We also obtain some accurate results for their properties, including degree distribution, clustering coefficient and network diameter, exactly according to the proposed generation algorithm of the networks considered, and discuss them. The network representation approach provided here can be used to investigate the complexity of many real-world systems from the perspective of complex networks.