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Table 1: Fundamental Graph Terminology and ConceptsTable 2: Types of Graphs and Graph ClassificationsTable 3: Graph Representation MethodsTable 4: Graph Traversal and Search AlgorithmsTable 5: Graph Algorithms - Connectivity and StructureTable 6: Spanning Tree AlgorithmsTable 7: Centrality Measures and Node ImportanceTable 8: Community Detection and ClusteringTable 9: Matching and Assignment ProblemsTable 10: Graph Coloring and Planar GraphsTable 11: Graph Metrics and PropertiesTable 12: Special Graph Problems and NP-Complete ProblemsTable 13: Random Graphs and Network ModelsTable 14: Advanced Graph Analysis TechniquesTable 15: Graph Theory Applications Across DomainsReferencesFoundational Graph TheoryGraph Types and ClassificationsGraph Algorithms - Traversal and Shortest PathsGraph Coloring and Planar GraphsSpanning Trees and MST AlgorithmsWalks, Paths, and CyclesTrees and ForestsMatrix RepresentationsDegree and Handshaking LemmaDense and Sparse GraphsConnectivity and BridgesCentrality MeasuresCommunity DetectionMatching ProblemsGraph ColoringGraph MetricsSmall-World NetworksHamiltonian Problems and TSPCliques and Independent SetsEulerian Paths and Chinese PostmanRandom Graphs and Network ModelsGraph Isomorphism and AutomorphismSpectral Graph Theory and GNNsNetwork FlowApplications