Graph representation provides a more effective method for describing the underlying data relationships. Nonetheless, the vast majority of data consists solely of feature information without a corresponding graph structure, rendering graph representation techniques ineffective. Much of the existing research on graph data has concentrated on how to effectively characterize graph nodes, with little focus on how to adaptively construct internal structures and potential connections between the sample pairs. On the other hand, the existing graph construction techniques generate linear inter-instance affinity distributions based on a probabilistic perspective, which might not give a true picture of the relationships. To overcome the above problems, motivated by the fact that sample and inter-sample affinities can be viewed as the source and strength of the magnetic field, respectively, a novel tangent-based affinity measurement algorithm that utilizes a parameter to dynamically adjust the sparsity of the magnetic field is derived. In addition, Adaptive Magnetic-Graph Clustering (AMGC) is designed for graph representation and clustering. AMGC ensures instance-level and cluster-level consistency using a novel dual decoder, where the reconstructed graph retains local affinity and global topology, and contrastive learning defines new sample pairs based on positive-incentive noise, making the learned embedding more discriminative. Eventually, we perform empirical experiments to demonstrate the superiority of the model.