  The class of Koch fractals is one of the most interesting families of
fractals, and the study of complex networks is a central issue in the
scientific community. In this paper, inspired by the famous Koch fractals, we
propose a mapping technique converting Koch fractals into a family of
deterministic networks, called Koch networks. This novel class of networks
incorporates some key properties characterizing a majority of real-life
networked systems---a power-law distribution with exponent in the range between
2 and 3, a high clustering coefficient, small diameter and average path length,
and degree correlations. Besides, we enumerate the exact numbers of spanning
trees, spanning forests, and connected spanning subgraphs in the networks. All
these features are obtained exactly according to the proposed generation
algorithm of the networks considered. The network representation approach could
be used to investigate the complexity of some real-world systems from the
perspective of complex networks.
