Stochastic blockmodels are used to detect community structure in networks and generate synthetic networks. However, traditional blockmodels ignore vertex degree variation, which is common in real-world networks and can distort results. This paper introduces a degree-corrected blockmodel that accounts for degree heterogeneity, improving community detection performance. The model incorporates vertex degrees into the likelihood function, allowing for more accurate inference of group structures. The degree-corrected model outperforms the uncorrected version in both real-world and synthetic networks. The paper also proposes a heuristic algorithm for community detection using the degree-corrected model. The standard stochastic blockmodel assumes that edges between vertices depend only on their group memberships. It can produce various network structures, including disconnected components and communities with dense internal connections. However, it fails to capture degree heterogeneity in real-world networks, leading to poor results. The degree-corrected blockmodel addresses this by incorporating vertex degrees into the likelihood function, allowing for more accurate inference of group structures. The model is shown to perform better in both real-world and synthetic networks. The degree-corrected blockmodel is defined with parameters that control the expected degrees of vertices. The model is shown to preserve the expected number of edges between groups and the expected degree sequence of the network. The model is compared to the uncorrected version, and it is shown to perform better in both real-world and synthetic networks. The paper also discusses the use of the model in generating synthetic networks and its performance on different types of network structures. The paper concludes that the degree-corrected blockmodel provides a more accurate representation of real-world networks and is better suited for community detection tasks. The model is also more flexible and can be used to generate synthetic networks for benchmarking. The paper highlights the importance of incorporating degree heterogeneity in network analysis and suggests that future research should explore more sophisticated blockmodels that incorporate degree sequences.Stochastic blockmodels are used to detect community structure in networks and generate synthetic networks. However, traditional blockmodels ignore vertex degree variation, which is common in real-world networks and can distort results. This paper introduces a degree-corrected blockmodel that accounts for degree heterogeneity, improving community detection performance. The model incorporates vertex degrees into the likelihood function, allowing for more accurate inference of group structures. The degree-corrected model outperforms the uncorrected version in both real-world and synthetic networks. The paper also proposes a heuristic algorithm for community detection using the degree-corrected model. The standard stochastic blockmodel assumes that edges between vertices depend only on their group memberships. It can produce various network structures, including disconnected components and communities with dense internal connections. However, it fails to capture degree heterogeneity in real-world networks, leading to poor results. The degree-corrected blockmodel addresses this by incorporating vertex degrees into the likelihood function, allowing for more accurate inference of group structures. The model is shown to perform better in both real-world and synthetic networks. The degree-corrected blockmodel is defined with parameters that control the expected degrees of vertices. The model is shown to preserve the expected number of edges between groups and the expected degree sequence of the network. The model is compared to the uncorrected version, and it is shown to perform better in both real-world and synthetic networks. The paper also discusses the use of the model in generating synthetic networks and its performance on different types of network structures. The paper concludes that the degree-corrected blockmodel provides a more accurate representation of real-world networks and is better suited for community detection tasks. The model is also more flexible and can be used to generate synthetic networks for benchmarking. The paper highlights the importance of incorporating degree heterogeneity in network analysis and suggests that future research should explore more sophisticated blockmodels that incorporate degree sequences.