% Checks whether a graph is simple (undirected, no self-loops, no multiple edges, no weighted edges)

%

% INPUTs: adj - adjacency matrix

% OUTPUTs: S - a Boolean variable; true (1) or false (0)

%

% Other routines used: selfLoops.m, multiEdges.m, isDirected.m

% Last updated: September 23, 2012

function S = isSimple(adj)

S = true;

if isDirected(adj) || selfLoops(adj) > 0 || multiEdges(adj) > 0 || length(find(adj > 1));

S = false;

end

%!test

%!shared T

%! T = load_test_graphs();

%!assert(isSimple(T{1}{2}),false)

%!assert(isSimple(T{2}{2}),true)

%!assert(isSimple(T{3}{2}),false)

%!assert(isSimple(randomGraph(randi(5)+20,rand)),true) % simple graph

%!assert(isSimple(edgeL2adj([1,2,2])),false) % multi-edge

%!assert(isSimple( [1 0 0; 0 0 1; 0 1 0]),false) % matrix with loops

%!assert(isSimple([0 1 1; 1 0 0; 0 1 0]),false) % directed matrix

%!demo

%! % undirected binary tree

%! isSimple([0 1 1; 1 0 0; 1 0 0])

%! % a weighted graph example

%! isSimple([0 2 1; 2 0 0; 1 0 0])

%! % directed graph example

%! isSimple([0 1 1; 0 0 0; 0 0 0])