A box-covering Tsallis information dimension and non-extensive property of complex networks. (March 2020) - Ramirez-Arellano, Aldo; Hernández-Simón, Luis Manuel; Bory-Reyes, Juan
Highlights: The definition of Tsallis information dimension is modified to propose a box-covering Tsallis information for complex networks. An approach to compute the entropic parameter is introduced. Based on this information measure and the entropic parameter, the classification of several real complex networks is assigned. Abstract: In this article, a box-covering Tsallis information dimension is introduced, and the physical interpretation of this new dimension has been assigned. Moreover, based on the introduced parameter q →, a characterization of non-extensive networks is stated, allowing the classification according to super-extensive ( q → ≺ 1 ), sub-extensive ( q → ≻ 1 ) or extensive ( q → = 1 ). The experimental results on both synthetic and real complex networks shed light on the type of interaction of the boxes. The results support the conjecture that the box-covering Tsallis information dimension is a suitable and flexible measure of information of real complex networks that exhibit a rich structural diversity.