different objects, identical network structure

In this post a quick example showing that completely different objects can have identical network/matrix structure.

So, let's look at some BKO:

friends |Alex> => |Jason> + |Ed> + |Mary> + |Liz> + |Beth> + |James> + |nathan>
friends |Bill> => |Jason> + |Beth> + |lena> + |John> + |nathan>
friends |Harry> => |charlie> + |bella> + |sam> + |smithie> + |david> + |nathan>

links-to |url 1> => |url k> + |url g> + |url b> + |url f> + |url l> + |url e> + |url j>
links-to |url 2> => |url h> + |url l> + |url b> + |url g> + |url i>
links-to |url 3> => |url m> + |url a> + |url d> + |url c> + |url n> + |url l>

So, they look a little alike, but not identical. But check out their matrix representations:

sa: matrix[friends]
[ bella   ] = [  0     0     1.00  ] [ Alex  ]
[ Beth    ]   [  1.00  1.00  0     ] [ Bill  ]
[ charlie ]   [  0     0     1.00  ] [ Harry ]
[ david   ]   [  0     0     1.00  ]
[ Ed      ]   [  1.00  0     0     ]
[ James   ]   [  1.00  0     0     ]
[ Jason   ]   [  1.00  1.00  0     ]
[ John    ]   [  0     1.00  0     ]
[ lena    ]   [  0     1.00  0     ]
[ Liz     ]   [  1.00  0     0     ]
[ Mary    ]   [  1.00  0     0     ]
[ nathan  ]   [  1.00  1.00  1.00  ]
[ sam     ]   [  0     0     1.00  ]
[ smithie ]   [  0     0     1.00  ]

sa: matrix[links-to]
[ url a ] = [  0     0     1.00  ] [ url 1 ]
[ url b ]   [  1.00  1.00  0     ] [ url 2 ]
[ url c ]   [  0     0     1.00  ] [ url 3 ]
[ url d ]   [  0     0     1.00  ]
[ url e ]   [  1.00  0     0     ]
[ url f ]   [  1.00  0     0     ]
[ url g ]   [  1.00  1.00  0     ]
[ url h ]   [  0     1.00  0     ]
[ url i ]   [  0     1.00  0     ]
[ url j ]   [  1.00  0     0     ]
[ url k ]   [  1.00  0     0     ]
[ url l ]   [  1.00  1.00  1.00  ]
[ url m ]   [  0     0     1.00  ]
[ url n ]   [  0     0     1.00  ]

I personally think that is cool, and kind of pretty.
Also has the consequence that if you map out the neural structure of some set of neurons then it is very hard to go from structure alone to finding the meaning of that structure.