1. Warm up 10-22-2010 1. Mr. Euler and Mr. Hamilton sit down one day to invent a game. They call their new game “baseball.” They argued about whether it was more important to run on the base paths or to touch the actual bases. Who ended up winning the argument? 2. A “circuit board” is an electronic piece of equipment involved in all kinds of technology. The electricity that passes through a circuit board starts at the power source and travels through the circuit back to the power source. How come we don’t call it a “path board?”

2. Vertex Edge Graphs Day 3: Adjacency Matrices An adjacency matrix is a ___________ way of displaying the data shown in a ____________. Graphical Vertex Edge Graph

3. Consider the following social network below. What could it represent? ____________________________ Alex Debra J.C. Justin Steph Lisa Phone Calls, Texts, letters, emails, Facebook posts, conversations, etc.

4. What do the arrows represent in this vertex edge graph? ________________ And arrow towards a person means what? ________________ An arrow away from a person means what? ________________ An arrow on both ends means what? ________________ Some type of connection or contact. They received a communication. They sent a communication. They both received and sent a communication.

5. Vertex Edge Graph vs. Adjacency Matrix The vertex edge graph is convenient to use when comparing two pieces of information. An adjacency matrix is more useful when comparing all the information or when comparing several parts at once.

6. First you must define your values: ► 1 in a row means ______________________________________ ► 0 in a row means ______________________________________ ► 1 in a column means ______________________________________ ► 0 in a column means ______________________________________ A connection was made/sent to the person in the column No connection was made/sent to that person. That person received a communication. No communication was received.

7. Now fill in your Adjacency Matrix LisaStephJustinJ.C.DebraAlex Total Total Lisa 0110114 Steph 1010103 Justin0001113 J.C.0010001 Debra0001102 Alex0001102 Total11335215 What do these totals tell us? The totals of the rows are the number of messages sent. The totals of the columns are the number of messages received.

8. Answer the following questions. Answers will vary. ► Who is the most “outgoing” or “outspoken/written?” _____________________________ ► Who is the “most popular?” _____________________________ ► Who is the “least popular?” _____________________________ ► Who is the most “introverted?” ______________________________

9. Example 2 Given this tournament graph, make an adjacency matrix to determine 1 st, 2 nd, 3 rd, and 4 th place. CalTresJustinAlTotalCal00101 Tres10102 Justin00000 Al11103 Al took 1 st, Tres was 2 nd, Cal was 3 rd, and Justin was 4 th.

10. Example 3 Given this tournament graph, made an adjacency matrix to determine 1 st, 2 nd, 3 rd, and 4 th place. BoKatJustinDanTotalBo00101 Kat10012 Justin01001 Dan10102 This one is a little different, we don’t know the clear winner without thinking a bit. You can still make your matrix and find the row sums.

11. ► The row sums tells us we can have ______ winners, they are _________ or _________. ► Now we need to list the Hamilton Paths (there are five) ► ___________, _________ and ________ ► Which one matches the matrix the best? Why ? BoKatJustinDanTotal Bo00101 Kat10012 Justin01001 Dan10102 2 Kat Dan BJKD DJKB KDBJ According to our matrix, Bo and Justin have to finish 3 rd and 4 th while Kat and Dan have to finish 1 st and 2 nd. KDBJ most closely matches that situation.

12. Summary: An adjacency matrix is used to… Homework: Adjacency Matrix w/s