This work explores the configurations of complex networks that would exhibit the maximum entropy using both degree and cyclic entropies measures. Theoretical models for such networks were proposed and were validated by using our developed genetic algorithms. A complex network configuration with the maximum cyclic entropy was identified as a cyclic star network; a star network with all non central nodes is connected with a ring. Also GA results within a small statistical error conclude the existence of an irregular network of size 8 that has higher cyclic entropy than the cyclic star. A complex network with a uniform distribution topology has the maximum degree entropy as expected is identified using a deterministic algorithm.