Scale free graphs have attracted attention by their non-uniform structure that can be used as a model for various social and physical networks. In this paper, we propose a natural and simple random model for generating scale free interval graphs. The model generates a set of intervals randomly under a certain distribution, which defines a random interval graph. The main advantage of the model is its simpleness. The structure/properties of generated graphs are analyzable by relatively simple probabilistic and/or combinatorial arguments, which is different from many other models. Based on such arguments, we show for our random interval graph that its degree distribution follows a power law, and that it has a large average clustering coefficient. © 2009 Elsevier B.V. All rights reserved.
Miyoshi, N., Shigezumi, T., Uehara, R., & Watanabe, O. (2009). Scale free interval graphs. Theoretical Computer Science, 410(45), 4588–4600. https://doi.org/10.1016/j.tcs.2009.08.012