AUTHOR=Wang Xiaomin , Ma Fei , Yao Bing TITLE=Dense Networks With Mixture Degree Distribution JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.647346 DOI=10.3389/fphy.2021.647346 ISSN=2296-424X ABSTRACT=

Complex networks have become a powerful tool to describe the structure and evolution in a large quantity of real networks in the past few years, such as friendship networks, metabolic networks, protein–protein interaction networks, and software networks. While a variety of complex networks have been published, dense networks sharing remarkable structural properties, such as the 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 a power-law form and below which the exponential distribution is observed. Next, we also prove the networks proposed to show the 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 the mean first-passage time increases logarithmically with the number of vertices of our networks.