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Explore the application of graph theory in investigating material genes and structural chemistry of Li-ion batteries in this comprehensive lecture. Delve into cutting-edge interdisciplinary research methods, including the development of a material big data system, to address fundamental questions about material genes in lithium-ion batteries. Examine structural chemistry based on graph theory, big data in materials science, and the concept of lithium-ion battery material genes. Investigate super-exchange interactions of d-orbital spinning electrons in transitional metals and learn about structure characterizations using large scientific facilities such as synchrotron and neutron radiation. Gain insights into new paradigms for material research aimed at advancing the development of critical materials for lithium-ion batteries. Reference key studies on structural degradation in Li-rich layered oxide cathodes, in situ Raman spectroscopy of interfacial water, the role of cobalt in developing Co-free Ni-rich cathodes, and the structural origin of high voltage instability in lithium cobalt oxide.