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function v = bfs_builtin (A, s)
%BFS_BUILTIN breadth-first-search using purely built-in methods
%
% v = bfs_builtin (A, s)
%
% A is a square binary matrix, corresponding to the adjacency matrix of a
% graph, with A(i,j)=1 denoting the edge (i,j). Self loops are permitted, and
% A may be unsymmetric. s is a scalar input with the source node. The output
% v is the level each node in the graph, where v(s)=1 (the first level), v(j)=2
% if there is an edge (s,j) (the 2nd level), etc. v(j)=k if node j is in the
% kth level, where the shortest path (in terms of # of edges) from s to j has
% length k+1. The source node s defaults to 1.
% SuiteSparse:GraphBLAS, Timothy A. Davis, (c) 2017-2022, All Rights Reserved.
% SPDX-License-Identifier: Apache-2.0
[m, n] = size (A) ;
if (m ~= n)
error ('A must be square') ;
end
n = size (A,1) ;
v = zeros (n,1) ;
if (nargin < 2)
s = 1 ;
end
% ensure A is binary, and transpose it
AT = spones (A') ;
q = zeros (n,1) ;
q (s) = 1 ; % q is the current level
for level = 1:n
% assign the level to all nodes in q
v (q ~= 0) = level ;
% find all neighbors of q, as a binary vector
qnew = spones (AT * q) ;
% discard nodes in qnew that are already seen
qnew (v ~= 0) = 0 ; %#ok
% move to the new level
q = qnew ;
% stop if the new level is empty
if (~any (q))
break ;
end
end
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