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| Research on Measurement of High-order Topology Structure of Patent Cooperation Based on Simplex and Its Association with Innovation Output |
| Guo Jianming1,2, Yang Alex Jie1,2, Song Xinyu1,2, Liu Qian1,2, Deng Sanhong1,2 |
1.School of Information Management, Nanjing University, Nanjing 210023
2.Key Laboratory of Data Engineering and Knowledge Services in Provincial Universities (Nanjing University), Nanjing 210023 |
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Abstract In an innovation environment where teamwork and collaboration are deepening, describing the patent cooperation network from the structural level and revealing its influence on innovation output have become important topics in innovation intelligence research. Existing research is mostly based on the perspective of binary relationships; therefore, it is difficult to describe the common group cooperation structure in patent cooperation. This paper introduces a high-order network representation method in algebraic topology, systematically describes the multi-agent interaction structure in the patent cooperation network, and examines the association between its higher-order structural features and inventors’ innovative outputs. Based on more than 7 million patent records in the PatentsView database, this paper constructs a simplex complex model of the patent cooperation network and uses a topological quantization method to measure the high-order structural characteristics of the network. Among them, the number of disconnected components β? is used to characterize the basic connectivity of the cooperative network, and the high-order loop β? is used to characterize the group cooperation mode that cannot be filled by low-order cooperation. On this basis, this study constructs an inventor-application year panel dataset and employs negative binomial fixed-effects regression models to systematically assess how higher-order structural features are associated with multiple dimensions of innovative output, including technological productivity, total patent citations, five-year patent citations, and the number of patent claims. The results show that there is an inverted U-shaped relationship between the number of disconnected components β? in the patent cooperation network and the four innovation output indicators; that is, within a reasonable range, an increase in the number of components is positively correlated with the level of innovation output, but when the number of components is high, the correlation with innovation output shows a weakening trend. The high-order loop β? is positively correlated with the four innovation output indicators, suggesting that higher-order collaborative structures are closely linked to knowledge integration capabilities and technological innovation performance. The robustness analysis shows that the above conclusions are stable in different technical development stages and different technical fields and have strong universality.
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Received: 17 December 2025
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