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Unformatted text preview: CS 2800: Discrete Math Sept. 26, 2011 Lecture Lecturer: David Kempe Scribe: Eunsol & June 1 Directed v. Undirected Graphs Today we introduced directed and undirected graphs. Graphs are a very powerful representation in computer science, as almost anything can be represented by graphs. Will provide examples of each kind and explore types of questions that can be answered. 1.1 Examples of Undirected Graphs Undirected graphs have edges that represent symmetric relationships. Ie, if you are friends with someone, then they are friends with you. Examples naturally follow as: 1. Friendship Networks 2. Collaboration Networks 3. Roads connecting cities 4. Mathematical models 5. Computer Networks 1.2 Examples of Directed Graphs Directed graphs have edges that do not represent symmetric relationships. Eg, if Jane is better at chess than Bob, then Bob is not better at chess than Jane and the edge will be directed to represent that. Examples follow as: 1. Sent Emails/ dialed phone calls 2. Transportation Networks - airlines(jet stream), trains(one way tracks), etc 3. Infection and Transmission of Disease - spread of epidemics 4. Finite State Machines 5. Predator and Prey Relationships 6. Boss Hierarchy Note: Any undirected graph can be turned into a directed graph, just represent each edge in the undirected graph with two directed edges in a directed graph Note: Depending on what you are representing, certain constraints will be properties of the representative graph. For example, in predator-prey graphs, you would not expect a triangle. In a boss hierarchy graph, you would expect the graph to be a tree (ie, contain no cycles). 1 1.3 Questions For each of graphs, we can pose some interesting questions: Questions for undirected graphs: Friendships: Who are the most influential people?...
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