In this work, we study the topological transition in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states, on the network known as random geometric graph (RGG). In that approach, each node has two cultural states and each link has also two states. There are six possible combinations of pairs (two nodes connected by one link) and half of them are categorized as a satisfying combination and the other half are unsatisfying one. The control parameter of the model dictates the probability of link and node updates. The system presents two phases: the absorbing phase is reached when all pairs of nodes become satisfying and, on the other hand, the active phase is present when there are both satisfying and unsatisfying pairs of nodes in the network. We found that, along with the unsatisfying pair density, the assortativity coefficient can also be used as an order parameter of the model. Additionaly, the assortativity coefficient gives an intuitive picture of the features on the topological transition of the network. We also calculated the components and cultural domains to add another view on the topological transition of the network.