1. Warm Up – 4.1 - Tuesday Find the critical times for each vertex.
Give a priority list using the decreasing time algorithm. Then create a timeline using two processors.
Give a priority list using the critical time algorithm. Then create a timeline using two processors.

3. Not a network The graph to the right is NOT a network. Why Not?
What can we do to
make it a network?

4. This is a network! This is a network because there is a
path from every
vertex to every
other vertex.

5. Degrees of separation
Since a network is a connected graph, there is a path from every vertex to every other vertex. (Note it is not a complete graph, there is not an edge between each pair of vertices)
The length of the shortest path joining 2 vertices in a network is called the degree of separation. (count the number of edges)

6. Degrees of Separation How many degrees of Separation are between
A and C?
C and I?

7. Network Worksheet #1

8. Trees A tree is a network without any circuits.
Note: Our definition of circuit here is different than an Euler Circuit or a Hamilton Circuit.
The graph to the left has a general circuit starting
at C and following C, B, E, D, C. A circuit simply starts
and ends at the same vertex.

9. Not a tree!
Because this graph has a circuit, this network is not a tree!

10. The following are trees!
They have no circuits within the graph.

11. Key Properties of Trees
The single path property: In a tree, there is only one path connecting two vertices.
Notice if we have two paths then we also have a circuit and thus a non-tree.

12. Key Properties of Trees
All Bridges Property: In a tree, every edge is a bridge (Remember that a bridge is an edge that if removed, makes the graph disconnected).
The N-1 edges property: A tree with N vertices has N-1 Edges.

13. Key Properties of Trees
If a network satisfies one of those three properties then it satisfies all three, and is a tree! WOOT!
The single path property: In a tree, there is only one path connecting two vertices.
All Bridges Property: In a tree, every edge is a bridge (Remember that a bridge is an edge that if removed, makes the graph disconnected).
The N-1 edges property: A tree with N vertices has N-1 Edges.