In this paper, we use elements of graph theory and port-Hamiltonian systems to develop a modular dynamic model describing the hydraulic behavior of 4th generation district heating networks. In contrast with earlier generation networks with a single or few heat sources and pumps, newer installations will prominently feature distributed heat generation units, bringing about a number of challenges for the control and stable operation of these systems, e.g., flow reversals and interactions among

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... ps controllers, which may lead to severe oscillations. We focus thus on flexible system setups with an arbitrary number of distributed heat sources and end-users interconnected through a meshed, multi-layer distribution network of pipes. Moreover, differently from related works on the topic, we incorporate dynamic models for the pumps in the system and explicitly account for the presence of pressure holding units. By inferring suitable (power-preserving) interconnection ports, we provide a number of claims about the passivity properties of the overall, interconnected system, which proves to be highly beneficial in the design of decentralized control schemes and stability analyses.