Write the data members of Network implemented using Adjacency matrix. Each element of the matrix will have two fields
•	exists
•	weight
•	See the board
•	Now that we have the implementation let us write some of the member functions
•	Network(int n)
•	need to call the constructor of the matrix m with rows=n, columns=n as parameters
•	See the board for other functions such as
•	Add, input operator
•	Write down the rest of the functions on your own.
•	There are a lot of real life applications to graph theory
•	k-coloring problem
•	Optimization (typically, NP Hard)
•	Given a graph what is the minimum number of colors you will need to make sure that no adjacent vertices are of the same color
•	
•	Decision (typically NP-Complete, with few exceptions)
•	Given a graph can you use k colors and make sure that no adjacent vertices are of the same color
•	Exam scheduling is coloring problem
•	One node for every course
•	Edge between two nodes if there are students taking both the courses
•	color corresponds to a time slot
•	Euler circuit, Hamiltonian circuit, Travelling Salesman problem
•	Euler circuit can be done in polynomial time
•	Travelling Salesman problem is similar to Hamiltonian circuit problem, you have to visit every node exactly once. In addition, you have to minimize the distance traveled.
•	If you can solve Travelling Salesman problem in polynomial time, you can solve the Hamiltonian circuit problem in polynomial time.
•	P and NP
•	P corresponds to a class of problems that can be solved in polynomial time
•	NP corresponds to a class of problems whose solution can be checked in polynomial time.
•	P=NP?
•	We know that P is a subset of NP
•	NP-complete problems