How far can a rumor travel without shortcuts?

This work investigates the propagation of rumors through the Maki-Thompson model on a ring network with $n$ nodes, where each individual is connected to its $2k$ nearest neighbors. Unlike traditional approaches that focus on the inclusion of shortcuts to optimize dissemination in small-world networks, we adopt a complementary perspective by examining the process exclusively on the ring network structure. The main objective is to determine the optimal value of $k$ as a function of $n$ in order to maximize the spread of the rumor. Through an analysis that combines contrasting examples and numerical approaches, we demonstrate that the model exhibits behavior analogous to that of homogeneously mixed populations, provided that the degree $k(n)$ is of order $\ln(n)$.