Two-parameter fractional Tsallis information dimensions of complex networks.

• 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]