The application of Internet of Things (IoT) within industrial environments is fostering the adoption of the digital twin (DT) approach, applied at the edge of the network to handle heterogeneity stemming from siloed application management solutions and from protocols originated by different manufacturing tools and enterprise services. In this challenging context, network heterogeneity also represents a critical element that can significantly limit the design and deployment of DT-oriented applications. This article proposes the Application-driven digital twin networking middleware with the twofold objective of: 1) Simplifying the interaction among heterogeneous devices by allowing DTs to exploit IP-based protocols instead of specialized industrial ones and to enhance packet content expressiveness, by enriching data via well-defined standards. 2) Dynamically managing network resources in edge industrial environments, applying software defined networking to exploit the communication mechanisms most suitable to application requirements, ranging from native IP to more articulated based on packet content.