Graph has been proven to be an emerging tool for spectrum sensing (SS), with detection performance closely related to the graph characteristics. Existing graph-based SS has been mainly investigated based on the unweighted graph for single user scenario, which leads to the poor performance at the low signal-to-noise. To address this issue, we introduce a weighted graph-based cooperative spectrum sensing method in this letter. Specifically, a signal-to-weighted-graph (STWG) mechanism for multi-user is proposed, which converts the signals of different users into a single weighted graph. To characterize the features of the weighted graph, graph sparsity is employed to represent the graph connectivity, upon which a test statistic is constructed. Moreover, a simple but practical method is proposed to estimate the detection threshold. Experimental results verify the theoretical analysis and demonstrate the superior performance of the proposed method.