Graph embedding preserves the graph properties while representing the input graph in a low-dimensional vector space. Multiple works have tried to solve this task using random walk-based methods. However, their neglect of a balanced sampling step often results in weak performance. In this manuscript, we introduce a novel algorithm called \(\beta \) -random walk to master the node embedding for the link prediction task. It consists of two main components that work as a single unit to perform the embedding task. On the one hand, we assign a parameter \(\beta \) to every node in the graph. This parameter balances the sampling stage by pushing the walker toward unvisited nodes instead of plugging the process into a random method. On the other hand, we design a weighting mechanism to produce at each episode a new weight for each sampled node. Our algorithm is based entirely on the \(\beta \) parameter for sampling and weighting, making it straightforward to train and stabilize. In the link prediction task, our algorithm unequivocally exhibits better results in precision and area under the curve relative to state-of-the-art baselines on the PubMed and Cora datasets.