Efficient Structures for Innovative Social Networks

What lines of communication among members of an organization are most effective in the early, ideation phase of innovation? We investigate this question with a recombination and selection model of knowledge transfer operating through a social network. We measure cost in human time, and seek efficient social network structures in the time - total cost plane (minimize ideation time subject to an upper bound on total cost, or vice versa) and in the time - cost per period plane, with a similar interpretation. Our results suggest that efficiently innovative organizations look nothing like what one intuitively associates with standard formal organizations with strict and unchanging lines of communication, nor do they conform with what one might expect from static social network representations of communication patterns. Rather, ideation is accelerated when people dynamically churn through a large (ideally the entire population) set of conversational partners over time, which naturally begets short path lengths and eliminates information bottlenecks. In organizations with these features group meetings do not help and can hurt the process, because many parallel conversations can achieve the same or better results as one-to-many communications. A family of networks called the complete wheel-stars emerges as an important family on the time-cost efficient frontier. Wheel-star graphs have a completely connected clique of agents at the center, with all other agents connected to the core but not to each other; the star and the complete graph are its extreme elements. We discuss the consequences of these results for organizations and sociometric analyses