Can we recognize an innovation?: Perspective from an evolving network model

‘Innovations’ are central to the evolution of societies and the evolution of life. But what constitutes an innovation? We can often agree after the event when its consequences and impact over a long term are known whether something was an innovation or not, and whether it was a ‘big’ innovation or a ‘minor’ one. But can we recognize an innovation ‘on the fly’ as it appears? Successful entrepreneurs often can. Is it possible to formalize that intuition? We discuss this question in the setting of a mathematical model of evolving networks. The model exhibits self-organization, growth, stasis, and collapse of a complex system with many interacting components, reminiscent of real world phenomena. A notion of ‘innovation’ is formulated in terms of graph-theoretic constructs and other dynamical variables of the model. A new node in the graph gives rise to an innovation provided it links up ‘appropriately’ with existing nodes; in this view innovation necessarily depends upon the existing context. We show that innovations, as defined by us, play a major role in the birth, growth and destruction of organizational structures. Furthermore, innovations can be categorized in terms of their graph-theoretic structure as they appear. Different structural classes of innovation have potentially different qualitative consequences for the future evolution of the system, some minor and some major. Possible general lessons from this specific model are briefly discussed.