A novel gravity model for vital node identification of complex network based on community distance and attribute importance

Gravity model is an effective method for vital node identification of complex networks. Many existing gravity models take the shortest path length as the interaction distance, however, interactions for the node pairs with identical path lengths may be different, and simply using the shortest path length cannot well distinguish the interaction difference. Moreover, although some models integrate multiple attributes as the node mass, they overlook the importance difference in the attributes. In this article, we propose a novel gravity model based on community distance and relative importance of attributes. The model introduces a community distance, where the nodes are classified into communities. For the nodes in different communities, we employ the graph machine learning to obtain the node features, and integrate the feature difference between the node pair into the shortest path to define the community distance, which therefore can better depict the node interactions. Then, we define the node mass based on three centralities describing the nodes’ local structural and path attributes, where the relative importance of the attributes is evaluated by the centrality information entropy. Experiments on nine realworld datasets show that the proposed algorithm is effective in identifying vital nodes compared with twelve baseline methods.