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.

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

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

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)

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

Network Worksheet #1

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.

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

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

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.

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.

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.