Agenda 2030 and Sustainable Development Goals (SDGs) are critical pieces of climate change communication. #FridaysForFuture (FFF) is one of the movements with the most coverage. This paper analyzes the network structure generated in Twitter by the interactions created by its users about the 23 September 2022 demonstrations, locates the most relevant users in the conversation based on multiple measures of intermediation and centrality of Social Network Analysis (SNA), identifies the most important topics of conversation regarding the #FridaysForFuture movement, and checks if the use of audio-visual content or links associated with the messages have a direct influence on the engagement. The NodeXL pro program was used for data collection and the different structures were represented using the Social Network Analysis method (SNA). Thanks to this methodology, the most relevant centrality measures were calculated: eigenvector centrality, betweenness centrality as relative measures, and the levels of indegree and outdegree as absolute measures. The network generated by the hashtag #FridaysforFuture consisted of a total of 12,136 users, who interacted on a total of 37,007 occasions. The type of action on the Twitter social network was distributed in five categories: 16,420 retweets, 14,866 mentions in retweets, 3151 mentions, 1584 tweets, and 986 replies. It is concluded that the number of communities is large and geographically distributed around the world, and the most successful accounts are so because of their relevance to those communities; the action of bots is tangible and is not demonized by the platform; some users can achieve virality without being influencers; the three languages that stood out are English, French, and German; and climate activism generates more engagement from users than the usual Twitter engagement average.