Novel evolving small-world scale-free Koch networks

On the basis of Koch networks that were constructed using Koch fractals, we propose a family of Koch networks with novel features that include an initial state that is a complete graph with an arbitrary number of nodes as a generalization of a triangle. In the subsequent evolutionary step, existing nodes create finite complete graphs. The analytical expressions for the degree distribution, clustering coefficient, average path length, and degree correlations are obtained. This family of Koch networks follows a power-law distribution, and has a large clustering coefficient, a small average path length, and degree correlations with rich properties. The networks can be assortative, disassortative, or uncorrelated under certain parameters that satisfy specific relationships