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This approach avoids central coordination, enhances data privacy and eliminates the risk of a single point of failure. Our research highlights that the effectiveness of decentralised federated learning is significantly influenced by the network topology of connected devices and the initial conditions of the learning models. We propose a strategy for uncoordinated initialisation of the artificial neural networks based on the distribution of eigenvector centralities of the underlying communication network, leading to a radically improved training efficiency. Additionally, our study explores the scaling behaviour and the choice of environmental parameters under our proposed initialisation strategy. 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