To get a directed graph, you should use digraph function. In order to do so, you have to build a standard square adjacency matrix describing how your nodes are connected. This is one way to do it (choosing to put the column nodes first in the adjacency matrix):
nNodeCol = size(A,2); % one node for each column of A
nNodeLine = size(A,1)/2; % one node for every two lines of A
% First the column nodes, then the line nodes:
nodeNames = [cellstr(strcat('column', num2str((1:size(A,2))'))) ; cellstr(strcat('line', num2str((1:size(A,1)/2)')))];
% Adjacency matrix adj, adj(i,j)=1 means there is an edge from node#i to node#j:
adj = zeros(nNodeCol+nNodeLine); % square matrix which size is the number of nodes
adj(1:nNodeCol, nNodeCol+1:end) = A(1:2:end,:)'; % edge from a column node to a line node is added for all the 1 in the first line of the node in the matrix
adj(nNodeCol+1:end, 1:nNodeCol) = A(2:2:end,:); % edge from the line node to a column node is added for all the 1 in the second line of the node in the matrix
% Here is your graph:
G = digraph(adj,nodeNames);
plot(G);
