Relationship Between the Fractal Dimension and the sum of edge Lin-Lu-Yau Ricci Curvatures on two types of fractal model networks

We aim to study the relationship between the fractal dimension and the Lin-Lu-Yau Ricci curvature in complex networks in this paper. We analyzed two types of networks with fractal properties, and compared the total edge Lin-Lu-Yau Ricci curvature with the fractal dimension of the complex networks from a global point of view. Except for a special case of one type of fractal network (i.e., a tree graph), we observed a quantitative relationship with the diameter of the network, thereby linking two important properties of complex networks. We found that the sum of the Lin-Lu-Yau Ricci curvatures of tree graphs is constantly 2. These properties provide a new perspective for analyzing complex networks and help us better understand their characteristics.