2D Square Lattice Hamiltonian Matrix

I want to construct a 2D Square Lattice Hamiltonian Matrix which consist of an on site parameter 'E' and nearest neighbour hopping parameter 't'. If there are 10*10 lattice sites than the matrix will be 100*100 for 2D lattice. Basically, I want to construct a map in which every site has 4 nearest neighbours in the bulk and the boundaries are open which means on the boundaries there are less than 4 nearest neighbours. Can anyone suggest me the way out of it?

Thanks in advance.