We propose a Degree-Corrected Block Model with Dependent Multivariate Poisson edges (DCBM-DMP) to study stock co-jump dependence. To estimate the community structure, we extend the SCORE algorithm in Jin (2015) and develop a Spectral Clustering On Ratios-of-Eigenvectors for networks with Dependent Multivariate Poisson edges (SCORE-DMP) algorithm. We prove that SCORE-DMP enjoys strong consistency in community detection. Empirically, using high-frequency data of S&P 500 constituents, we construct two co-jump networks according to whether the market jumps and find that they exhibit different community features than GICS. We further show that the co-jump networks help in stock return prediction.