Tsallis entropy analysis in spatial networks with applications to wireless networks

Abstract A new method is proposed for analyzing complexity and studying the information in spatial networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of the random connection model on the point process which is obtained by connecting the points with a probability that depends on their relative positions. By applying information theory and conditional discussion, the bounds for Shannon and Tsallis entropies are derived for the ensemble of these spatial networks. Using this function and Lagrange’s optimization formula, the connection function that maximizes Tsallis entropy under general constraints is obtained. A simulation example is provided to demonstrate the practical application of this method in the analysis of ad hoc wireless networks. By considering the obtained results, it can be stated that the wireless networks that adhere to the studied model are almost maximally complex. Also, Tsallis conditional entropy maximizing function is compared with other connection functions using numerical studies and the optimal value for the maximization of conditional entropies is obtained.