As an important and challenging problem in machine learning and computer vision, multilabel classification is typically implemented in a max-margin multilabel learning framework, where the inter-label separability is characterized by the sample-specific classification margins between labels. However, the conventional multilabel classification approaches are usually incapable of effectively exploring the intrinsic inter-label correlations as well as jointly modeling the interactions between inter-label correlations and multilabel classification. To address this issue, we propose a multilabel classification framework based on a joint learning approach called label graph learning (LGL) driven weighted Support Vector Machine (SVM). In principle, the joint learning approach explicitly models the inter-label correlations by LGL, which is jointly optimized with multilabel classification in a unified learning scheme. As a result, the learned label correlation graph well fits the multilabel classification task while effectively reflecting the underlying topological structures among labels. Moreover, the inter-label interactions are also influenced by label-specific sample communities (each community for the samples sharing a common label). Namely, if two labels have similar label-specific sample communities, they are likely to be correlated. Based on this observation, LGL is further regularized by the label Hypergraph Laplacian. Experimental results have demonstrated the effectiveness of our approach over several benchmark data sets.