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CSE 321 Discrete Structures Winter 2008 Lecture 25 Graph Theory
Graph formalism –G = (V, E) –Vertices –Edges Directed Graph –Edges ordered pairs Undirected Graph –Edges sets of size two
Graph examples Communication Networks Road networks
Social networks Community Graph –Linked In, Face Book Transactions –Ebay Authorship –Erdos Number
The web graph
Page Rank Determine the value of a page based on link analysis Model of randomly traversing a graph –Weighting factors on nodes –Damping (random transitions)
Graph terminology NeighborhoodDegree
Degree sequence Find a graph with degree sequence –3, 3, 2, 1, 1 Find a graph with degree sequence –3, 3, 3, 3, 3
Directed Degree Theorem
Special Graphs Complete Graphs K n Cycle C n Hypercube Q n Mesh M n,m
2-coloring A graph is two colorable iff all cycles have even length
Graph Representations Adjacency Lists Adjacency Matrices Incidence Matrices
Strong connectivity vs. Weak Connectivity
Strongly Connected Components
Counting Paths Let A be the Adjacency Matrix. What is A 2 ? d c b e a
Graph Isomorphism I Are these two graphs the same? ad cb w x y z
Graph Isomorphism II Are these graphs the same?
Graph Isomorphism III Are these graphs the same?
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