Network Dynamics of Innovation Processes

We introduce a model for the emergence of innovations, in whichcognitive processes are described as random walks on the network oflinks among ideas or concepts, and an innovation corresponds to thefirst visit of a node. The transition matrix of the random walk dependson the network weights, while in turn the weight of an edge isreinforced by the passage of a walker. The presence of the networknaturally accounts for the mechanism of the ``adjacent possible,'' andthe model reproduces both the rate at which novelties emerge and thecorrelations among them observed empirically. We show this by usingsynthetic networks and by studying real data sets on the growth ofknowledge in different scientific disciplines. Edge-reinforced randomwalks on complex topologies offer a new modeling framework for thedynamics of correlated novelties and are another example of coevolutionof processes and networks.