Cyclic Entropy of Complex Networks

We calculate the cyclic entropy of a real virtual friendship network to have an insight on the degree of its robustness. Upon counting the number of cycles of different sizes in the network, a probability distribution function is resulted. An actual friendship network is found to have cyclic entropy bounded between random and small-world networks models. It has dual properties. Small world networks indicate the existence of critical network sizes: 150 and 700 at which the cyclic entropy is minimum. Scale-free networks have the highest cyclic entropy among all other complex network models regardless of the size of the network.