Stochastic blockmodels are widely used for detecting community structure in networks and generating synthetic networks. However, most blockmodels ignore vertex degree variations, which can significantly distort results in real-world networks with broad degree distributions. This paper proposes a degree-corrected version of the stochastic blockmodel that incorporates vertex degree heterogeneity, leading to an improved objective function for community detection. The degree-corrected model outperforms the uncorrected model in both real-world and synthetic networks, as demonstrated through a heuristic algorithm. The degree-corrected model preserves the expected degree sequence and edge probabilities while allowing for more flexible group assignments, making it more suitable for networks with heterogeneous degree distributions. The paper also discusses the limitations and potential extensions of the degree-corrected blockmodel, including its application to more complex network structures and the need for methods to estimate the number of groups.Stochastic blockmodels are widely used for detecting community structure in networks and generating synthetic networks. However, most blockmodels ignore vertex degree variations, which can significantly distort results in real-world networks with broad degree distributions. This paper proposes a degree-corrected version of the stochastic blockmodel that incorporates vertex degree heterogeneity, leading to an improved objective function for community detection. The degree-corrected model outperforms the uncorrected model in both real-world and synthetic networks, as demonstrated through a heuristic algorithm. The degree-corrected model preserves the expected degree sequence and edge probabilities while allowing for more flexible group assignments, making it more suitable for networks with heterogeneous degree distributions. The paper also discusses the limitations and potential extensions of the degree-corrected blockmodel, including its application to more complex network structures and the need for methods to estimate the number of groups.