MATLAB: Adjacency matrix of a hexagonal graph

adjacency matrixhexagonal graphMATLAB

I am looking for an efficient way to compute the adjacency matrix of a hexagonal graph, so that away from the boundary the graph is 3-regular and its minimal cycles are hexagons. The graph is arranged in a rectangle with n vertices in each row and m rows. My follow on computations require me to represent this matrix as a sum of three separate adjacency matrices: one for the horizontal edges, one for the edges that slant in the 'North West' direction and one for the North East. I give my code below; I need to make the whole computation much quicker (this is one of many elements), so I would welcome any suggestions. Thank you. 
%% Hexagonal graph
% This function produces the adjacency matrix of a "rectangular graph" whose cells are hexagons. 
% The size of the graph is [n,m], where n is the number of vertices
% on one level and m is the number of levels. The adjacency matrix is 
% given in three parts: 
% H: the horizontal edges, 
% and, looking from the bottom: 
% NE: edges slanted "up and right", 
% NW: edges slanted "up and left"
function [H,NW,NE]  = HexGraphPart(n,m)
GridH  = zeros(n*m);  
GridNW = zeros(n*m); 
GridNE = zeros(n*m); 
% NW part: 
% odd numbered rows: 
for kk = 1:floor(m/2)
    for ii = 1:2:n
        if (2*kk-1)*n + ii <= n*m
            GridNW((2*(kk-1))*n+ii, (2*kk-1)*n + ii) = 1; 
        end
    end
end
% even numbered rows: 
for kk = 1:floor(m/2)
    for ii = 2:2:n
        if 2*kk*n +ii  <= n*m
            GridNW((2*kk-1)*n + ii , 2*kk*n + ii ) = 1; 
        end
    end
end
% NE part:
% Odd numbered rows: 
for kk = 1:floor(m/2)
    for ii = 2:2:n
        if (2*kk-1)*n + ii <= n*m
            GridNE(2*(kk-1)*n+ii, (2*kk-1)*n + ii) = 1; 
        end
    end
end
% Even numbered rows: 

for kk = 1:floor(m/2)
    for ii = 1:2:n
        if 2*kk*n +ii  <= n*m
            GridNE((2*kk-1)*n + ii , 2*kk*n + ii ) = 1; 
        end
    end
end
% Horizontal edges: 
% Odd numbered rows
for kk = 1: ceil(m/2) 
    for ii = 1:2:n 
        if 2*(kk-1) +ii +1 <= n*m
        GridH(2*(kk-1)*n +ii, 2*(kk-1)*n +ii +1) = 1; 
        end
    end
end
% Even numbered rows: 
for kk = 1:floor(m/2)
    for ii = 2:2:n-1
        if (2*kk-1)*n + ii + 1 <= n*m
            GridH((2*kk-1)*n + ii, (2*kk-1)*n + ii + 1) = 1; 
        end
    end
end
    H =  GridH + transpose(GridH); 
    NW = GridNW + transpose(GridNW); 
     NE = GridNE + transpose(GridNE); 
end

Best Answer

[A,B,C] = HexGraphPart2(7,8);
G = graph(A+B+C); 
figure;
plot(G);
function [H,NW,NE]=HexGraphPart2(m,n)
[I,J]=ndgrid(1:m,1:n);
K = I + (J-1)*m;
p=m*n;
H = sparse(K(1:2:end-1,1:2:end),K(2:2:end,1:2:end),1,p,p) + ...
    sparse(K(2:2:end-1,2:2:end),K(3:2:end,2:2:end),1,p,p);
NW = sparse(K(1:2:end,1:2:end-1),K(1:2:end,2:2:end),1,p,p) + ...
     sparse(K(2:2:end,2:2:end-1),K(2:2:end,3:2:end),1,p,p);
NE = sparse(K(1:2:end,2:2:end-1),K(1:2:end,3:2:end),1,p,p) + ...
     sparse(K(2:2:end,1:2:end-1),K(2:2:end,2:2:end),1,p,p);
H=H+H';
NW=NW+NW';
NE=NE+NE';
end
NOTE:1 Your code is buggy with certain combination of m/n
NOTE2: the code can be simplied !if you only need A+B+C
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