In this paper, we address the issue of how different personalities interact in Twitter. In particular we study users’ interactions using one trait of the standard model known as the “Big Five”: emotional stability. We collected a corpus of about 200000 Twitter posts and we annotated it with an unsupervised personality recognition system. This system exploits linguistic features, such as punctuation and emoticons, and statistical features, such as followers count and retweeted posts. We tested the system on a dataset annotated with personality models produced from human judgements. Network analysis shows that neurotic users post more than secure ones and have the tendency to build longer chains of interacting users. Secure users instead have more mutual connections and simpler networks.