The making of mathematical connections in the classroom plays a dual role. While many studies highlight the importance of connections for the learning of mathematics, others inform of students' difficulties associated with the making of connections. This study aims to characterise the mathematical connections that arise in habitual classroom practice, using an inductive approach, in the context of introducing integers with pupils aged 12-13. Results show that connections emerge as networks of links resulting from interactions between the teacher and the students. We present a definition of connection, a detailed characterisation of their internal structure as networks of links and a global characterisation which takes into account the role of the connection in the context in which it takes place. The complementarity of the two characterizations allows us to coordinate, from a classroom perspective, existing specific classification proposals for connections with a broader notion of connection used by relevant curricular guidelines. Factors that may determine the complexity of connections and may be related with students' difficulties when dealing with connections in the classroom are also discussed.