**5. Conclusions**

The purpose of this study was to approach the understanding of the complexity of water governance through three properties, namely diversity, nestedness, and dynamics, in jurisdictional and temporal scales and at different levels. For this, we built the Water Governance Complexity Framework based on some elements of the Kooiman Interactive Governance Framework [14,28]. We used the domestic water supply system in Oaxaca to show the operability of the proposed framework in addressing the complexity of water governance. We discovered that the properties of diversity, nestedness, and dynamics and their respective proxies when intertwined can provide good approximations of the non-linear interactions, emergence, and constant change that classify water governance as complex. The importance of this study and the Water Governance Complexity Framework is that it offers a way to understand the complexity of water governance due to historical processes without automatically assuming that water governance is complex, which limits and biases any conclusions or future improvement efforts.

The Water Governance Complexity Framework proposed in this study is not fixed. We recommend that the framework be used as a methodological guide by which new proxies can be incorporated to address the diversity, nestedness, and dynamics properties (e.g., the flow of knowledge and power dynamics) and new properties. New proxies may emerge from testing the framework in other regions or contexts and from advances in complexity theory. Additionally, a more refined level of analysis can be included in the framework, such as that at the individual level, which allows for a more profound understanding of complexity regarding how the stakeholders make decisions, how they implement specific actions, and how they interact with other stakeholders. Exploring the individual level will allow us to determine if the stakeholders of different jurisdictional levels participate in cross-level interactions from a legitimate non-hierarchical condition (different from how we assume nestedness) and the importance of leadership in inducing, resisting, or adapting to institutional change [75]. Despite the criticism of the theory of complexity when applied to social systems [76], we believe in its usefulness to diagnose the complexity of the water governance of any system, be it the water supply systems for domestic, agricultural, or industrial use. This practicality of the framework can help decision makers and practitioners generate a deeper understanding of water governance that allows for legal reforms, new laws, and new public policies to be created, along with changes to desirable models (e.g., polycentrism) based on the knowledge of current stakeholders and institutions and the historical context. This research reinforces the idea that water governance is complex, while inviting us to question this complexity and the elements and properties responsible for it.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/2073-444 1/13/20/2870/s1. Table S1. Structure of the survey used in this study. We employed four questions and their possible answers. In the answers, the "others" option was left not to limit the eventual appearance of different stakeholders at the local level. Table S2. Matrix used to note the answers obtained from interviewing stakeholders regarding cross-level and internal interactions in the communities to carry out ten activities of the first and second governance orders. Table S3. Matrix of binomial presence (1)/absence (0) data resulting from the collapse of the results obtained from all the interviewees and the ten activities of each community. Table S4. Results of the binomial presence/absence matrix of the communities that are municipal seats responsible for the water supply system for domestic use. This matrix was used to carry out the nesting analysis with the NODF (Nestedness based on the Overlap and Decreasing Fill) metric in NeD software. Table S5. Results of the binomial presence/absence matrix of the communities that are municipal agencies or that have a water committee responsible for the water supply system for domestic use. This matrix was used to carry out the nesting analysis with the NODF (Nestedness based on the Overlap and Decreasing Fill) metric in NeD software. Table S6. Open-ended questions of the semi-structured interviews were applied to elders and experts to identify possible institutional changes related to water for domestic use in rural communities.

**Author Contributions:** Conceptualization, F.G.-G.; methodology, F.G.-G., A.S.-A., G.H.-A., C.M.-A., M.A.M.-J. and D.M.-R.; formal analysis, F.G.-G.; investigation, F.G.-G. and G.H.-A.; resources, F.G.-G. and G.H.-A.; data curation, F.G.-G.; writing—original draft preparation, F.G.-G.; writing—review and editing, A.S.-A., G.H.-A., C.M.-A., M.A.M.-J. and D.M.-R.; supervision, A.S.-A.; project administration, F.G.-G.; funding acquisition, F.G.-G., A.S.-A., G.H.-A., C.M.-A., M.A.M.-J. and D.M.-R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Geographic Society (grant number EC-62227R-19) and The National Council of Science and Technology of Mexico (CONACYT) through Doctorate Grants awarded to the first author.

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

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** We thank the communities of Oaxaca who participated in this study for their support and openness. We also thank the team of the Marine and Coastal Ecosystems Governance and Management Laboratory of the CIIDIR- Oaxaca unit of the Instituto Politécnico Nacional (IPN) for helping with the community surveys and for facilitating transportation. We are also deeply grateful for the suggestions made by three anonymous reviewers that helped us improve the scope of this work.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.
