Assessment of the Effectiveness of Random and Real-Networks Based on the Asymptotic Entropy

Recently, the analytical study of the structural properties of complex networks has attracted increasing attention due to the growth of these real-world networks. Mathematical graph theory helps to understand and predict their behavior. This paper examines and compares the structural properties such as the small-world effect, the clustering coefficient and the degree distribution of Erdos-Renyi random networks with some real-world networks. Besides, we propose an algorithm to calculate the number and the entropy of spanning trees of these networks by using the electrically equivalent transformations. The result allows us to evaluate the robustness and the homogeneity of their structure. The proposed technique is efficient and more general compared to the classical ones.