Dense Networks With Mixture Degree Distribution - Wang, Xiaomin; Ma, Fei; Yao, Bing (Frontiers in Physics, 2021)
Complex networks have become a powerful tool to describe the structure and evolution in large quantity of real networks in the past few years, such as friendship networks, metabolic networks, protein-protein interaction networks, software networks and so on. While a variety of complex networks have been published, dense networks sharing remarkable structural properties, such as scale-free feature, are seldom reported. Here, our goal is to construct a class of dense networks. Then, we discover that our networks follow the mixture degree distribution, that is, there is a critical point above which the cumulative degree distribution has power-law form and below which the exponential distribution is observed. Next, we also prove the networks proposed to show small-world property. Finally, we study random walks on our networks with a trap fixed at a vertex with the highest degree and find that the closed form for mean first-passage time increases logarithmically with the number of vertices of our networks.