Week 4: Lab Document, 9/20
Let G be a graph with vertex set V and edge set E.
For any vertex v in G, the clustering coefficient of v, denoted C(v),
is the ratio of the number of edges between pairs of neighbors of v to
the total number of pairs of neighbors of v.
For example, say vertex v has 10 neighbors.
Then v has (10 choose 2) = 45 pairs of neighbors and suppose that of these pairs of neighbors
15 pairs are connected by edges. Then the clustering coefficient of v is 1/3.
If a vertex has one or no neighbors, let us define its clustering
coefficient to be 1.
The clustering coefficient of G, denoted C(G), is the average
of the clustering coefficients of all the vertices in G.
The value of C(v), for any v, is between 0 and 1 and therefore the value of
C(G) is also between 0 and 1.
Problem:

Add the following two methods to the myGraph class
to respectively compute the clustering coefficient of a given vertex and the clustering
coefficient of the graph.
public double clusteringCoefficient(String v)
public double clusteringCoefficient()

Test your implementation of the clusteringCoefficient
methods on the Ladders graph, described below.
Later we will use the Ladders graph to play the Ladders game.
In this twoplayer game, one player chooses a starting word and an ending
word and the other player constructs a "ladder" between the two words.
A ladder is a sequence of words that starts at the starting word, ends
at the ending word, and each word in the sequence (except the first) is
obtained from the previous word by changing a letter in a single position.
For example, suppose the starting word is flour and the
ending word is bread, then a ladder between these two
words is: flour, floor, flood,
blood, brood, broad, bread.
Here is the link that will take you to a file
called words.dat
that contains 5757 five letter English words.
This word list comes from Stanford Graphbase, a collection of
interesting data sets and graph algorithms put together by Donald E. Knuth.
The original file can be found here.
This word list is the database that your program will use to construct the
Ladders graph.
The Ladders graph should contain a vertex for every word in the file
and an edge between every pair of vertices that differ in exactly one
position.
To construct the graph, you should call the function addVertex
on every word in the file and then the function addEdge for every
edge you want to add.
Finally, after constructing the Ladders graph, compute its clustering
coefficient.