Summary: Simulations of consensus formation in networks of interacting agents have recently demonstrated that convergence to a small number of opinion clusters is more likely when the network is adaptive rather than static. In order to better model realistic social networks, we have extended an existing model of such a process, by the introduction of a parameter representing each agent’s level of ‘authority,’ based on their opinion relative to the overall opinion distribution. Here we aim to determine the importance of initial network topology for opinion formation in this model, using two distinct initial network topologies: an Erdős-Rényi random network, and the Watts-Strogatz small-world network. It is shown that marked differences exist in statistics of the model after opinion convergence. These include the number of interactions between agents needed to reach consensus, as well as a clear influence of opinion tolerance on the network’s clustering coefficient, mean shortest path, and degree distribution after convergence. This latter effect suggests some interesting possibilities regarding the topology of ‘converged’ networks.