This work studies the interaction networks that arise on Twitter in relation to such a relevant topic as climate change. We detected that the largest connected component of these networks presents low values of average degree and betweenness, as well as a small diameter compared to the total number of nodes in the network. The largest connected component of retweeting and quoting networks also exhibits very low negative assortativity. The quoting and retweeting networks have a more hierarchical structure than the (...) replying network. We also find that the process of emergence of new links in the interaction networks can be properly modeled through a Support Vector Machine model using the embeddings provided by the Node2Vec algorithm. A Random Forest model using certain similarity measures as explanatory variables between nodes also provides high accuracy. In addition, we analyze the communities existing in each interaction network by means of the Louvain method. The cumulative probability distributions of hashtags per community are also examined. (shrink)