topological_order.m

function perm=topological_order(A,varargin)
% TOPOLOGICAL_ORDER Returns the topological ordering of vertices in a dag
%
% perm=topological_order(A) generates a permutation of the vertices that
% indices a topological order.  A topological order satisfies the property
% that edge (i,j) in A implies i comes before j in the order.  A
% topological order only exists for directed acyclic graphs.  If A is not a
% directed acyclic graph, then the returned perm is empty.
%
% This method works on directed graphs.
% The runtime is O(V+E).
%
% ... = topological_order(A,...) takes a set of
% key-value pairs or an options structure.  See set_matlab_bgl_options
% for the standard options. 
%   There are no additional options for this function.
%
% Note: this function does not depend upon the non-zero values of A, but
% only uses the non-zero structure of A.
%
% Example:
%   n = 10; A = sparse(1:n-1, 2:n, 1, n, n); % construct a simple dag
%   p = topological_order(A);
%
% See also TEST_DAG

% David Gleich
% Copyright, Stanford University, 2007-2008

%% History
%  2008-09-23: Reformatted common section. 
%  2008-10-07: Fixed example.
%%

[trans check full2sparse] = get_matlab_bgl_options(varargin{:});
if full2sparse && ~issparse(A), A = sparse(A); end
if check, check_matlab_bgl(A,struct()); end
if trans, A = A'; end

[perm dag] = topological_order_mex(A);

% in this case it wasn't a dag
if dag == 0
    perm = [];
end