Degree-based entropies of networks revisited

Studies on the information content of graphs and networks have been initiated in the late fifties based on the seminal work due to Shannon and Rashevsky. Various graph parameters have been used for the construction of entropy-based measures to characterize the structure of complex networks. Based on Shannon’s entropy, in Cao et al. (Extremality of degree-based graph entropies, Inform. Sci. 278 (2014) 22–33), we studied graph entropies which are based on vertex degrees by using so-called information functionals. As a matter of fact, there has been very little work to find their extremal values when considered Shannon entropy-based graph measures. We pursue with this line of research by proving further extremal properties of the degree-based graph entropies.