Topological network features determine convergence rate of distributed average algorithms.

Gossip algorithms are message-passing schemes designed to compute averages and other global functions over networks through asynchronous and randomised pairwise interactions. Gossip-based protocols have drawn much attention for achieving robust and fault-tolerant communication while maintaining simplicity and scalability. However, the frequent propagation of redundant information makes them inefficient and resource-intensive. Most previous works have been devoted to deriving performance bounds and developing faster algorithms tailored to specific structures. In contrast, this study focuses on characterising the effect of topological network features on performance so that faster convergence can be engineered by acting on the underlying network rather than the gossip algorithm. The numerical experiments identify the topological limiting factors, the most predictive graph metrics, and the most efficient algorithms for each graph family and for all graphs, providing guidelines for designing and maintaining resource-efficient networks. Regression analyses confirm the explanatory power of structural features and demonstrate the validity of the topological approach in performance estimation. Finally, the high predictive capabilities of local metrics and the possibility of computing them in a distributed manner and at a low computational cost inform the design and implementation of a novel distributed approach for predicting performance from the network topology.