Abstract
δ-Hyperbolicity is a graph parameter that shows how close to a tree a graph is metrically. In this work, we propose a method that reduces the size of the graph to only a subset that is responsible for maximizing its δ-hyperbolicity using the local dominance relationship between vertices. Furthermore, we empirically show that the hyperbolicity of a graph can be found in a set of vertices that are in close proximity and that concentrate in the core of the graph. We adopt two core definitions each of which represents a different notion of vertex coreness. The minimum-cover-set core, which is a transport-based core, and the k-core, which is a density-based core. Our observations have crucial implications on computing the δ-hyperbolicity of large graphs. (Parts of this work were published in Alrasheed (On the δ-hyperbolicity of complex networks. In: Proceedings of the IEEE/ACM international conference on advances in social networks analysis and mining (ASONAM), 2016).)
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Notes
- 1.
All experiments in this work were performed on a personal computer with an Intel(R) 2.50 GHz CPU and 16 GB Ram without the use of multiprocessors.
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Alrasheed, H. (2018). δ-Hyperbolicity and the Core-Periphery Structure in Graphs. In: Özyer, T., Alhajj, R. (eds) Machine Learning Techniques for Online Social Networks. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-89932-9_2
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