**5. Conclusions**

Today, globalization and networking characteristics of international collaboration activities are particularly prominent. A systematic investigation of global TWC networks will substantially further our understanding in this field. Based on the mining of cooperation events data, the article builds the Post-Cold War era global TWC networks. Through the comprehensive use of social network analysis and QAP analysis methods, the topological structure and spatial pattern of TWC are revealed, and the multidimensional proximity mechanism of TWC is discussed. The analysis shows that:

First, in terms of the overall scale of TWC events, the annual change in the number of events was often not linear, mostly fluctuating. The number of events in 1992 was the peak over the years since 1948, and then the scale of events experienced a process of rapid decline and stable fluctuation. However, compared with the Cold War era, the overall scale of TWC events in the Post-Cold War era has increased significantly. The key reasons for these characteristics are the reconstruction of territorial space on the eve of the end of the Cold War and the change in the international system.

Second, in terms of the TWC network structure, the roles of different network actors are different, and the spatial heterogeneity of the TWC linkages is obvious. In the frequency network of TWC, the dominant countries are mostly distributed in Asia, Africa, Europe, and North America, but especially in Asia. China, Egypt, Germany, the United States, and Russia are the most important network nodes. Network ties are concentrated in the Eastern Hemisphere, especially the Eurasian continent and the African continent. Additionally, the extra-regional powers are widely involved in the TWCs of both the Eurasian and African continents. In the intensity network of TWC, the geographical proximity of the network has become more obvious, and the high strength linkages are further concentrated in a few regions. Countries located in the Amur, Mekong, Ganges, Indian, Aral Sea, Jordan, and the Nile River Basin have carried out high-intensity water cooperation.

Third, in terms of the proximity mechanism, TWC activities among state actors are not only affected by a single dimension of proximity, but by the comprehensive influence of multidimensional proximity. Overall, geographical proximity, economic proximity, organizational proximity, and colonial proximity significantly affect the intensity of water cooperation among countries. Specifically, the capital distance between countries is negatively correlated with the intensity of TWC. Whether countries belong to the same transboundary basin, the bilateral trade volume, the number of water organizations existing among countries, whether there is a colonial relationship between countries, and whether there is a common colonizer have significant positive effects on the intensity of TWC.

Fourth, spatial and regression analysis examined our theoretical framework for the influence of different dimensions of proximities on the generation of global TWC. This framework discusses the general process and mechanism of global TWC from the perspective of proximity, as well as the complex interaction and causal mechanisms. State actors are the main actors involved in global TWC, and close interaction and cooperation are carried out among and within the various actors. The formation and deepening of TWC depend on the willingness and ability of the actors. Both of them are indispensable and constitute sufficient conditions for TWC results. Cooperative willingness and ability are affected by multidimensional proximities, which are composed of various constituent elements. Each proximity can not only play an independent role, but also promote the development of the actor's cooperative willingness and ability through appropriate combinations.

The global TWC network is a kind of complex and dynamic network. Based on the feasibility of data mining and cleaning, the time scale analyzed in this paper mainly covers the period from 1992 to 2013. It is still necessary to further update the data, especially since 2013, since with China's proposal and implementation of the Belt and Road Initiative, the international cooperation pattern of Asia, Africa, and Europe is being profoundly reshaped. Therefore, although the current networks have shown the spatial pattern of in-depth combination with the core region of the Belt and Road Initiative, it is of positive significance to further research the new characteristics of TWC under the background of the Belt and Road Initiative. In addition, with the strengthening of interdependence and globalism, the deeper economic ties between countries are increasingly shaping both social and environmental ties, and the systematic correlation between different networks will become deeper. Therefore, further strengthening the research on the effects of linkage between TWC networks and other networks, such as energy trading network and food trading network, will help to understand the systemic effects and global governance underlying the background of globalization.

**Author Contributions:** Conceptualization, Z.Y., X.Q. and D.D.; methodology, Z.Y. and X.Q.; software, Z.Y.; validation, Z.Y. and X.Q.; formal analysis, Z.Y., X.Q. and S.G.; investigation, Z.Y. and X.Q.; resources, D.D.; data curation, Z.Y.; writing—original draft preparation, Z.Y.; writing—review and editing, Z.Y., X.Q. and S.G.; visualization, Z.Y.; supervision, D.D.; project administration, D.D.; funding acquisition, Z.Y. and D.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDA20100308), and China Scholarship Council (grant no. 202006140025).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We would like to thank the three anonymous reviewers for their invaluable comments and suggestions. We are also grateful to Professor Malcolm McPherson for his thoughtful comments on a prior version of this article and his selfless help in improving it.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

**Table A1.** The intensity scale of TWC events [47].

