Knowledge percolation threshold and optimization strategies of the combinatorial network for complex innovation in the digital economy

Digital economy expands the source of knowledge for innovation and accelerates the flow and combination of knowledge to form novel knowledge combinations, thereby generating the interdisciplinary knowledge production model. In this context, complex innovation which is characterized by the knowledge production consequence based on the combinations of multiple-field knowledge has become the new way for firms to seize new development opportunities and compete in the digital economy. Given that complex innovation emerged from a gradually forming large, multilayered, combinatorial network consists of collaboration networks in various knowledge fields that are initially separated, the challenge of facillatating the emergence of complex innovation is unveiling the minimum proportion of connected paths in the combinatorial network to trigger effective transmission of multi-fields knowledge and offering applicable optimization strategies to optimize that proportion. This study incorporated Ohm's law into the percolation theoretical framework and calculate the knowledge percolation threshold of the combinatorial network and its subnetworks with patent data of Chinese strategic emerging industries. We further examined the optimization results of six strategies in terms of their optimization effects and time costs. Accordingly, we revealed the probability of knowledge percolation occurring in a combinatorial network and its subnetworks, clarified knowledge transmission characteristics according to knowledge-based cluster dynamics, and determined strategies for optimizing the knowledge percolation threshold. This study is not only highly feasible and exercisable for academics to conduct future studies, but it also has vital implications for the practitioners to utilize and control the knowledge transmission of the combinatorial network to realize the complex innovation.