Key node identification in complex networks using gravity model based on motif and non-negative matrix factorization

The identification of key nodes is a research hotspot in complex networks. To find nodes that are critical to network structure and function, various methods have been proposed. Among these, the gravity model is an effective approach based on local and path information. However, the traditional gravity model uses node degree as mass to determine local information, which only reflects first-order relationships between nodes. Additionally, the path information in the model primarily focuses on the geographical distance between nodes, overlooking the issue of inefficient distance calculations in high-dimensional networks. To address these issues, this paper proposes a motif and non-negative matrix factorization-based gravity centrality (MNMFGC) method. First, we use motifs to capture higher-order relationships between nodes and replace the traditional adjacency matrix with a motif-based adjacency matrix, which more comprehensively considers the higher-order correlations between nodes. Next, we apply non-negative matrix factorization (NMF) to obtain low-dimensional representations of the nodes, enabling us to extract underlying structural information between nodes and calculate distances more efficiently. In the simulation experiments, the Susceptible-Infected-Recovered (SIR) model is used to evaluate MNMFGC, and the results confirm its effectiveness.