Two-parameter fractional Tsallis information dimensions of complex networks

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.