Week 3 - Homework

Using your programming language of choice develop a set of classes or functions that will allow to read in, store and perform certain calculations on graphs. With these classes or functions, you should then write a program that will read in a graph from a file, print out a representation of the graph and then do some calculations on the graph. Details follow:

Reading in Graphs

A graph will be provided in a text file in the form:

A B
A B
A D
A C
D B
D F

where each line represents an edge between two nodes. Note that node names are alphanumeric and of arbitrary length, and that there can be an arbitrary number of nodes and edges. Note that for this homework, you only need consider undirected graphs.

Representing Graphs

This is up to you, though if you're working in C++, Python or Java it would be good to have classes for nodes and edges. If you're working in C, you could use struct's. In any case, you'll want to implement methods or functions that will let you do things like

See if there is an edge containing a specified node
Check whether a node exists
Get the edge containing the two nodes
Count the number of edges connected to a node (i.e., vertex degree)

Calculations on Graphs

You should implement the following functions

getAdjacencyMatrix - returns an adjacency matrix for the graph
getDistanceMatrix - return a matrix whose (i,j) element is the shortest topological distance between nodes i and j. To implement this you'll need to implement the Floyd-Warshall algorithm (assume that edge costs are 1).
getClusteringCoefficient - return the clustering coefficient for a given node. Use it to calculate the average clustering coefficient for the graph. See class notes or the Wikipedia page
getDegreeCentrality - return the degree centrality of the graph (consider using the adjacency matrix)

You do not need to check for cycles or loops. Once you have these functions, write a program that reads in a graph specified in a file and then calls the functions for the graph that you read in and prints the output with an informative message. Implement the code yourself and do not use implementations from other libraries.

Evaluation

The homework is worth 40 points and the breakdown is as below

20 - Implementing the above requirements
15 - Correctness of the output on new graphs
5 - Cleanliness of the code, comments, capturing edge cases

To test your code, I've provided three graphs graph1.txt, smallworld.txt and estnodes.txt. I will test your code on some new graphs, so ensure that when you write the code, you can handle general cases and errors - that is, your program should not crash!.

Submitting

Tar or zip your source code and include a README indicating how the code should be compiled or run. Email it to me at rguha@indiana.edu.

The due date for this homework is 12th February

Rajarshi Guha

Last modified: Mon Jan 19 20:42:32 EST 2009