Collaborative problem solving (CPS) is an important skill enabling students to co-construct knowledge and tackle complex problems through group interactions. While the importance of group interactions in CPS is well recognized, it is unclear how the emergence of generative artificial intelligence (GAI), with advanced cognitive support, may alter group dynamics in CPS. This study bridges this gap by examining group interactions in GAI-supported CPS, focusing on the structural patterns and interaction content characterizing students' social dynamics. Six groups of three to five students used an online messaging tool with a GPT-4.0 enabled chatbot for a CPS activity. Group interactions were modelled using network analysis and interaction content was coded into socio-emotional, cognitive, metacognitive, and coordinative dimensions. Employing a network assortativity measure and a binomial test to the interactions among students and the GAI chatbot, we identified a GAI-centred interaction pattern in which students tended to interact significantly more with the chatbot than their peers in the collaborative problem-solving process. Students' interactions with the chatbot involved primarily cognitive interactions but also metacognitive and socio-emotional interactions. This study introduces novel network methods to analyse small group interactions and contributes new empirical evidence and theoretical insights into the social influence of GAI tools, emphasizing the need for further investigations on the factors influencing interaction dynamics among students and GAI tools in collaborative learning.