Historically, algebraic methods treat many types of graphs efficiently. Her work initiated a geometric approach to spectral graph theory with connections to differential geometry. According to the biography Fan Rong K Chung Graham, "Spectral graph theory studies how the spectrum of the Laplacian of a graph is related to its combinatorial properties.". In 1997, the American Mathematical Society published Chung's book Spectral graph theory. This book became a standard textbook at many universities and is the key to study Spectral graph theory for many mathematics students who are interested in this area. Fan Chung's study in the spectral graph theory brings this “algebraic connectivity” of graphs into a new and higher level. Network science Fan Chung's work in random graph models shed new light on the field of network science. Many real-world large information networks (such as Internet Graphs, Call Graphs, and Collaboration Graphs, etc.) have been observed to be well approximated by a power law distribution. Fan Chung's work in the Chung-Lu model, pioneered the theory of treating random graphs with arbitrary degree distributions, including the power law graphs. Her work provides a solid framework for quantitative and rigorous analysis for modeling and analyzing large complex networks. It also often serves as a popular benchmark for comparing new graph models in network science. In 2006, the American Mathematics Society and the Conference Board of the Mathematical Sciences co-published Fan Chung and Linyuan Lu's book Complex Graphs and Networks. The book gave a well-structured exposition for using combinatorial, probabilistic, spectral methods as well as other new and improved tools to analyze real-world large information networks. Quasi-random graphs Fan Chung, together with Ronald Graham and Richard Wilson, introduced a strong notion of equivalence among graph properties through the control of error bounds and developed the theory of quasi-random graphs. In a series of research papers (with several coauthors), she showed that a large family of graph properties is equivalent in the sense that if a graph satisfies any one of the properties, it must satisfy all of them. The set of equivalent quasi-random properties includes a surprisingly diverse collection of properties, and therefore provides efficient methods for validating graph properties. Many (but not all) random graph properties are quasi-random. The notion of quasi-randomness has been extended to many other combinatorial structures, such as sequences, tournaments, hypergraphs and graph limits. In general, the theory of quasi-randomness gives a rigorous approach to 'random-like'