We argue that in Barcelona there is a multiplicity of innovative projects and experiences that go beyond Henry Etzkowitz and Loet Leydesdorff's (2000) "triple helix" model of innovation. The research results point to the coexistence of dominant innovation practices and emerging innovation practices. Both formats shape relationships between policy, technologies and market, deploying differentiated, but not opposing, innovation practices. Combining concepts from actor-network theory, ethnographic observations and network visualization techniques, we propose an approach to innovation that is more inclusive of the diversity of collective formats that create and manage socio-material arrangements or innovations