To explain the dynamics of technological transitions, we develop a model where agents enjoy positive network externalities from using the same technology, while some agents, called entrepreneurs, ignore these externalities and introduce new technologies. We assume that technologies form a graph which is evolving because entrepreneurs create new nodes. Remaining agents make decisions about technology and only adopt a new technology if it gives higher returns net of the switching costs. Technologies can be recombined. Re-combinatorial innovations create short-cuts which speed up technological progress, allowing transitions that are impossible otherwise. Our model replicates some stylized facts of technological transitions, such as punctuated equilibria, path dependency and technological lock-in. A theoretical analysis shows that entrepreneurs can always break a technological lock-in, though the time required rises exponentially with the population size. We find analytically a critical mass of innovators for successful innovations and technological transitions. Recombinant innovation counters network externalities, and calls for technological diversity as a key feature of technological transitions. An extensive simulation experiment shows that stronger network externalities are responsible for S-shaped utility and technological quality curves, indicating that a threshold of innovation probability is necessary to boost innovation. We finally introduce a policy view and interpret the innovation probability as the effort to foster technological change. A welfare measure including innovation costs presents an optimal interior value of innovation effort, which follows from the S-shape of the utility and indicates that neither too low or too high efforts are advisable for innovation policy. The optimal innovation effort is strongly correlated with the number of recombinations, which further indicates how recombinant innovation is important in achieving a sustained technological progress at relatively low costs.