Estimating the relative importance of nodes in complex networks based on network embedding and gravity model

Identifying nodes that hold relative importance in complex networks is a burgeoning research area. Previous studies have demonstrated the effectiveness of the gravity model in capturing interactions among nodes in high-dimensional network space. Traditional algorithms predominantly concentrate on structural characteristics and node random walks in high-dimensional network space, overlooking substantial computational overhead and intricacies within the high-dimensional space. Simultaneously, the rapid evolution of the Internet has given rise to a series of emerging technologies, such as embedding models that can map high-dimensional network nodes to low-dimensional vector space. To address this issue, we introduce a novel algorithm for quantifying node relative importance, denoted as the Network Embedding and Gravity Model (NEGM). First, the network embedding method transforms nodes into low-dimensional, real-valued, dense vectors in Euclidean space. Then, drawing inspiration from Newton's law of universal gravitation, it proposes a novel gravity model. Finally, utilizing the novel gravity model, it calculates the aggregate attractive force of all nodes within the target node set. Experimental results show that NEGM excels in measuring the relative importance of nodes in various types of networks, demonstrating its significant potential for mining deep-seated information within authentic networks like protein networks and criminal networks.