This paper argues the role of the University in the Smart City transformation strategy. The theoretical structure takes as reference the recent Complexity theory for city development and their application to the networks of the Connected city. The approach is based on a justified selection of Barcelona and its four universities. We carry out a deductive and interpretivist method interviewing 19 senior experts whole profiles represent the different forces of the Triple Helix model. Our results show the Barcelona city hall has the objective to implement five main innovative services which are fuelled by six main emerging technologies. Nevertheless, we demonstrate that the universities curriculum is not aligned with the city hall's objectives and a gap exists to prepare the undergraduates to the professions required for the Smart City. We recommend six propositions to reshape the University program curricula and leverage the application of Complexity theory to network. The originality of this study is to propose a 3-phases method along with a framework with pre-filled templates and protocols of interviews to analyze universities that pursue the objective to support Smart Cities implementation in a new context of science of cities.