The Hasse diagram of the divisibility graph

30.svg

hasse_divisibility.py

def divisibility_graph( n ):
	E = set()
	for dst in range( 30 ):
		for src in range( 2, dst ):
			if dst % src == 0:
				E.add( ( src, dst ) )
	return E

def hasse_diagram( E ):
	E2 = set()
	for e0 in E:
		for e1 in E:
			if e0[1] == e1[0]:
				E2.add( ( e0[0], e1[1] ) )
	return E - E2

def to_dot( E ):
	res = [ 'digraph G { rankdir = LR; ' ]
	res.extend( [ '{}->{};'.format( *e ) for e in E ] )
	res.append( '}' )
	return '\n'.join( res )

if __name__ == '__main__':
	from sys import argv
	E = divisibility_graph( int( argv[ 1 ] ) )
	H = hasse_diagram( E )
	print to_dot( H )

This code generates the Hasse diagram of the divisibility graph in Graphviz format. You can run it as

 python hasse_divisibility.py 30 | dot -Tsvg >h.svg