Graph-Based Cybersecurity

  1. Foundational Graph Theory
    1. Basic Graph Components
      1. Nodes and Vertices
        1. Node Definition and Properties
          1. Node Labels and Attributes
            1. Node Types and Classifications
            2. Graph Structure Elements
              1. Degree Concepts
                1. Node Degree Calculation
                  1. In-Degree and Out-Degree
                    1. Degree Distribution
                    2. Paths and Walks
                      1. Simple Paths
                        1. Complex Paths
                          1. Path Length Metrics
                          2. Cycles and Loops
                            1. Cycle Detection
                              1. Acyclic Properties
                              2. Connectivity Concepts
                                1. Connected Components
                                  1. Strong and Weak Connectivity
                                    1. Graph Reachability
                                2. Graph Types and Classifications
                                  1. Basic Graph Types
                                    1. Undirected Graphs
                                      1. Directed Graphs
                                        1. Mixed Graphs
                                        2. Weighted vs Unweighted Graphs
                                          1. Weight Assignment Strategies
                                            1. Weight Interpretation in Security
                                            2. Special Graph Types
                                              1. Multigraphs
                                                1. Hypergraphs
                                                  1. Bipartite Graphs
                                                    1. Property Graphs
                                                      1. Temporal Graphs
                                                    2. Important Graph Structures
                                                      1. Fundamental Patterns
                                                        1. Cliques and Complete Subgraphs
                                                          1. Independent Sets
                                                            1. Trees and Forests
                                                              1. Stars and Hubs
                                                                1. Chains and Paths
                                                                2. Complex Structures
                                                                  1. Communities and Clusters
                                                                    1. Hierarchical Structures
                                                                      1. Scale-Free Networks
                                                                        1. Small-World Networks
                                                                      2. Graph Representation Methods
                                                                        1. Adjacency Matrix Representation
                                                                          1. Adjacency List Representation
                                                                            1. Edge List Representation
                                                                              1. Incidence Matrix Representation

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                                                                            1. Introduction to Graph-Based Cybersecurity

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                                                                            3. Cybersecurity Domain Modeling