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CSE 222 Systems Programming

CSE 222 Systems Programming. Graph Theory Basics Dr. Jim Holten. Introduction. Basic Definitions Concepts and Algorithms Applications. Basic Definitions. Nodes aka Vertices Links aka Edges aka Arcs. Basic Definitions. Subgraphs Undirected vs Directed Graphs

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CSE 222 Systems Programming

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  1. CSE 222Systems Programming • Graph Theory Basics • Dr. Jim Holten

  2. CSE 222 Introduction • Basic Definitions • Concepts and Algorithms • Applications

  3. CSE 222 Basic Definitions • Nodes aka Vertices • Links aka Edges aka Arcs

  4. CSE 222 Basic Definitions • Subgraphs • Undirected vs Directed Graphs • Paths, Distances, and Graph Diameter • Connected Graphs • Components of a Graph • Fully connected graph or subgraph

  5. CSE 222 Undirected Graph

  6. CSE 222 Directed Graph

  7. CSE 222 Basic Definitions • Node Attributes aka Labels, Indices, Weights, Categories, etc. • Link Attributes aka Labels, Indices, Weights, Categories, etc. • A Semantic Graph is a graph partitioned based on node or link attribute values

  8. CSE 222 Semantic Graph Documents Authors Concepts

  9. CSE 222 More Definitions • A Hypernode replaces a collection of nodes and their included links. • A Hypergraph is any graph that includes one or more hypernodes.

  10. CSE 222 Example of Hypergraph Documents Authors Concepts

  11. CSE 222 Hypergraph of Social Network

  12. CSE 222 Some Concepts • A cluster is a subgraph made up of set of highly interconnected nodes. • A critical node is a node on a unique path between two nodes or subgraphs of interest. • A critical link is a link on a unique path between two nodes or subgraphs of interest.

  13. CSE 222 Related Algorithms • Finding clusters is defined many ways • Fully connected subgraph or just better than some threshold on connectedness? • Is a node only connected to a node in the cluster to be included in the cluster? • Finding critical paths, nodes, or links

  14. CSE 222 Related Concepts • Projections of nodes or subgraphs are mappings via directed links. • The domain subgraph includes the projection's "from" nodes. • The range subgraph includes the projection's "to" nodes. • Basis Node Set is a minimal set of nodes that have a path to every other node

  15. CSE 222 Projection Mapping

  16. CSE 222 Subset Projections

  17. CSE 222 Related Concepts • There are multiple ways of looking at a single collection of nodes and links. • Are multiple graphs just a single multi-component graph? • Interdependencies among multiple graphs can be useful.

  18. CSE 222 Interdependencies

  19. CSE 222 Applications • Software Organization • Activity Sequence Organization • Interactions between processes

  20. CSE 222 Software Organization • Flow charts • Data interdependencies • Interactions between processes

  21. CSE 222 Data Organization Chart

  22. CSE 222 Processes Organization Chart

  23. CSE 222 Activity Sequence Organization • Gantt and Pert charts • Project resource planning charts • Storyboarding

  24. CSE 222 Storyboard of theSoftware Development Process

  25. CSE 222 Network Modeling Applications • Communications (Internet, etc.) • Energy distribution (electric power, natural gas, etc.) • Transportation (highways, railways, waterways, etc) • Social associations • Financial and product flows

  26. CSE 222 Infrastructure Networks

  27. CSE 222 Critical InfrastructureInterdependencies

  28. CSE 222 Physics Models • Mesh Models • Space segmented into volumes • Volumes surrounded by faces and edges • Edges meet at vertices • Model element type dependencies form a graph of interdependent element sets

  29. CSE 222 Mesh Models

  30. CSE 222 Element Type Dependencies

  31. CSE 222 Graphs are a significant factor in the present and the future of computer science! Summary

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