The paper introduces *graph implementations* as a generic method for representing convex functions via their epigraphs within a disciplined convex programming (DCP) framework. This approach allows for the easy specification and efficient solving of a wide range of smooth and nonsmooth convex programs using interior-point methods. The authors propose a modeling framework called *cvx* that supports DCP and graph implementations, enabling users to specify models without needing to understand the underlying transformations. The framework includes a library of common convex and concave functions and can automatically transform models into solvable forms, calling appropriate numerical solvers. The paper also discusses the DCP ruleset, which ensures that transformations preserve convexity and efficiency, and provides examples of how graph implementations can be used to handle both smooth and nonsmooth functions, including the Huber penalty function and the square root function. The benefits of graph implementations are highlighted, particularly their ability to efficiently solve nonsmooth functions and their compatibility with conic solvers for smooth functions.The paper introduces *graph implementations* as a generic method for representing convex functions via their epigraphs within a disciplined convex programming (DCP) framework. This approach allows for the easy specification and efficient solving of a wide range of smooth and nonsmooth convex programs using interior-point methods. The authors propose a modeling framework called *cvx* that supports DCP and graph implementations, enabling users to specify models without needing to understand the underlying transformations. The framework includes a library of common convex and concave functions and can automatically transform models into solvable forms, calling appropriate numerical solvers. The paper also discusses the DCP ruleset, which ensures that transformations preserve convexity and efficiency, and provides examples of how graph implementations can be used to handle both smooth and nonsmooth functions, including the Huber penalty function and the square root function. The benefits of graph implementations are highlighted, particularly their ability to efficiently solve nonsmooth functions and their compatibility with conic solvers for smooth functions.