Non-planar unclustered Peterson graphs as scale-free models of the Internet of Things

Many real life networks present diameter logarithmic with the number of nodes and degree distribution that follow power law. Often these networks have also a modular and self-similar feature and usually associated with topological restrictions-their clustering is low, even zero, and they are almost non-planar. In the paper, we propose a generalized self-similarity growing network model. As the construction is deterministic, we can capture exact analytic expressions for relevant properties of the model including average degree, clustering coefficient, degree distribution, diameter, the number of leaves of every maximum leaf spanning tree. We make a conclusion that it is scale-free and small-world.