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You can call that a structural formula, because it is showing the arrangement of bonds between the atoms in a molecule. It tells you more than the plain chemical formula, which just tells you the atoms in a molecule, but less than a full three-dimensional model, which tells you exactly where each atom is located.
This is an organic structure formula, so it is simplified quite a bit: most of the carbon atoms are not drawn with actual letter C's, but are rather implied to exist wherever a bond ends and no other atom symbol is written. Most of the hydrogen atoms, and the bonds to them, are not drawn at all. Only the H atoms bonded to "heterotoms" like oxygen, nitrogen or sulfur are drawn, and even then usually the bond is omitted (so an H bonded to an O is just written as -OH). Finally, in many cases common groups like an amino group are condensed to just the group formula (NH2), because an experienced chemist knows how the atoms are bonded in these groups. All of this simplification is in order to show the essential characteristics of a molecule, in this case its carbon skeleton, without cluttering up the drawing.
If you are asking what that particular molecule actually is, it's an oligopeptide (a very short protein), and the amino acid sequence from top to bottom is Cys-Tyr-Ile-Gln-Asn-Cys-Pro-Leu-Gly. (I can't actually see the final glycine, as it's around the guy's side, but I assume it's there.) This molecule is called oxytocin, and it is a hormone strongly associated with sexual attraction and the bonding between mothers and newborn children.
Oooh, you're awesome.....
"organic structure formula" or "structural formula" is what I was looking for. I was thinking that there was an actual name for it, but I guess there isnt. There's the Lewis structure, but it's not exactly the same as what I was thinking. Thaaaaaaaaaaaaaaanks!!!!!!