Search

• Two-parameter fractional Tsallis information dimensions of complex networks based on q-logarithm is introduced. • The parameter β → and α → in the two-parameter fractional Tsallis information dimension are the interaction among the sub-systems and the interaction among the elements of each sub-system, respectively. • The index of interaction ι – formulated based on the α → and β → – captures the networks' complex topology. • The two-parameter fractional Tsallis information dimension is a more precise statistical index to measure the complexity of the complex networks than the fractional information dimensions. A two-parameter (namely, α → and β →) fractional Tsallis information dimensions of complex networks based on q − logarithm is introduced. The meanings assigned to such parameters are the quantification of the interaction among the elements (nodes) that are part of the same sub-system (sub-network) and the interaction among the sub-systems (sub-networks), respectively. Also, the index of interaction ι – formulated based on the α → and β → – captures the networks' complex topology. The result reveals that the percentage of synthetic and real-world complex networks for which the best model is the introduced two-parameter fractional Tsallis information dimensions are 76.5% and 81.25%, respectively, which support the conjecture that it is a finer measure that captures the complex interactions of the networks that fractional information dimensions. [ABSTRACT FROM AUTHOR]

• 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. 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. [ABSTRACT FROM AUTHOR]

Highlights • The concept of d-summable sets is applied in complex networks to measure fractal dimension. • The concept of d-summable sets has not yet been applied in complex networks. • The d-summable information model fits the covering of the network best for several examples. • Empirical evidence suggest that information dimension is not a universal model of real complex networks. Abstract In past two decades a wide range of complex systems, spanning many different disciplines, have been structured in the form of networks. Network dimension is a crucial concept to understand not only network topology, but also dynamical processes on networks. From the perspective of the box covering, volume dimension, information dimension, and correlation dimension several approaches have been proposed. We modify the commonly used definitions of the box dimension and information dimension to introduce a d-summable approach (a geometric notion that comes from geometric measure theory) of these dimensions. It is applied to calculate d-summable information dimension of several real complex networks. We offer empirical evidence to support the conjecture that d-summable information model worth carrying out than information model for several networks. [ABSTRACT FROM AUTHOR]