Chapter 9.2, Problem 9E

Consider again the graph accompanying Exercise 5 of Section 9.1, which we reproduce here.

1. For the graph on the left,

   1. Make a table that shows the least number of edges joining each pair of vertices in this graph(Such a table displays the least number of stops required on air trips between cities in the region depicted by the graph.)

   2. Add the numbers in each column of the table. Divide each column total by the degree of the corresponding vertex. These ratios are called accessibility indexes since they measure the relative accessibility of the cities (by air). Which city is the most accessible? Which is the least accessible?

   3. Suppose a direct flight joining cities $v_1$ and $v_2$ is introduced. What is the new beta index of the graph? What are the new accessibility indexes? Which city is most accessible now? Which city is now least accessible?

   4. Repeat part(iii), assuming a flight is introduced between cities $v_2$ and $v_6$ instead of between $v_1$ and $v_3$.

2. Repeat the preceding questions for the graph on the right.