Is the surface of a fluid more or less dense? Paper explaining why surface tension is parallel to the interface:

Away from the surface there is perfect force balance due to the symmetry around a molecule. Near the interface, however, the up-down symmetry is broken. To restore the force balance in the vertical direction, the upward repulsive arrow (dashed) has to balance the downward attractive arrow (solid). In the direction parallel to the interface, the symmetry is still intact, thus automatically ensuring a force balance parallel to the interface. This balance means that along the direction parallel to the interface, there is no reason why the attractive forces should have the same magnitude as the repulsive forces. In practice, the attractive forces are stronger, giving rise to a positive surface tension force.

This was the diagram provided in the paper:

This is my intuition for the question title: ( Is the density greater on the interface or less dense? )

Consider the molecule at the interface. The force balance on this molecule is broken creating a net force downwards that minimises surface area. However, because this molecule doesn't keep accelerating downwards it must eventually be balanced by the repulsive forces of molecules below. At this point where the attractive and repulsive forces are balanced the molecules must be more compact. Hence I think the surface of the fluid must be more dense than the bulk. Because the surface is denser than there exists more attractive forces giving rise to surface tension.

Is the above intuition correct and that a fluid's surface is indeed denser than the bulk? Or is there a flaw in the explanation above? If so, an alternative explanation would be extremely helpful.

Edit: There are varying explanations that seem to contradict themselves. Some answers state that the density is lower on the interface and that molecules attract each causing the surface to be under tension. Other answers state that the density is greater at the interface. Can someone tell me the true conclusion? To me, a higher density seems more intuitive because the attractive forces between molecules should decrease with distance. The central part of my question is to understand the true origin of surface tension at the molecular level.
 A: To the Density Question:
Whether the fluid density increases or decreases depends on the other phase involved. In your example the figure shows a liquid/vapour interphase. Since the density changes continuously from liquid to vapour, the liquid density has to decrease from it's liquid bulk value to it's vapour value. See the fig. below for a density profile of liquid n-Hexane in equilibrium with it's vapour. It shows the density plotted vs the vertical distance z. z=0 is here set to the vapour bulk density, z=infinity is the liuid bulkd density. An "s-curve" starting at low densities (vapour) and changing continuously to high density (liquid) also shows the size of the interface. The higher the temperature, the larger the interface. This goes up to the critical point, at which the interface gets infinitely large, or, equivalently, no difference between vapour and liquid can be detected anymore.

To the Surface Tension Question:
As already explained by others in this thread, in the bulk of a liquid phase one molecule has more neighbours to interact with than in the interface region. The bulk phase therefore is energetically more favourable as the potential energy of the system decreases. A ball drops down to earth as it's potential energy decreases (until repulsion from the ground kicks in), similarly, molecules approach each other until repulsion and attraction equal out, see L-J-Potential for example. Now, in the interphase region, due to the density decrease from bulk liquid to vapour, there are less neighbours for the molecules to interact with, therefore it requires energy to bring molecules from the (energeitcally favoured) bulk to the (less favoured) interphase. This means the system energy increases which makes it unvafourable. Thus, the system tries to decease it's interfacial area with the other phase in order to lower it's energy (e.g. the reason for spherical drop form, since spheres have the smallest surface/volume ratio).
Edit: 
Since Sources were asked for:
You'll find many if you search for "square gradient theory" or "density profile liquid/vapour" or sth similar. 
However, the theory to describe density profiles thermodynamically was originally developed by Van der Waals in 1893. 
It was extended by Cahn, Hilliard (1958) 
A nice book, which summarizes the results as well as the historical development of interfaceial thermodynamics is that by Rowlinson and Widom (1982)
A: The origin of surface tension is the intermolecular attraction of fluids. The actual answer to the question should be 'lower'. Just take a look at it, why is the density lower at the surface of a fluid.
Consider a round drop of a fluid (I am neglecting the presence of gravity and a container). Every molecule attracts every molecule in that droplet that results in a net attractive force towards the center of the drop. It is just like how the gravitational force of earth attracts everything to the core. I also want to replace the term 'downward force' with 'inward force' for a droplet. Now, the inward force on the molecules inside the bulk is greater because they are closer to the center while the inward force on the surface molecules is lower as they are far from the center.
As the intermolecular attraction force is weak on surface molecules and they feel repulsion from only one side, the molecules have greater kinetic energy than of the bulk molecules. In the bulk, molecules of the fluid experience strong intermolecular attraction and repulsion from every side that causes their kinetic energy to be lower. Having greater kinetic energy implies that surface molecules have greater average distance between them ('average' is used because its impossible to calculate distance between every pairs of molecule). And greater average distance means greater volume which implies less density.
Moreover, surface tension is mainly noticed in liquid and the liquid surface is not a sharp cutoff. There is liquid-vapour interface at the fluid surface. Surely, there is so much density difference between fluid and its vapour. The former has high density and the latter has lower density.
That is why the fluid surface has slightly less density than the bulk.
Image source
Origin of surface tension:
There is always a cohesive force between the molecules of the fluid and so the free surface of the fluid always try to stay with the least surface area. The molecules at fluid surface has the highest potential energy (Just like an object at the surface of earth has higher potential energy than any other object inside earth). If the density is higher at the surface, that means there exist a very high potential energy at the surface and the droplet will blow up or collapse to get lower potential in this case. But we see that the droplet remains the same, i.e it doesn't blow up or collapse. That means it always try to reduce its surface area and it has lower density at the surface. With lower surface area and lower density the potential energy stays at a balance. There is a nice wikipedia article on surface tension.
As of it, the fluid surface stays stretched and behaves like a streched curtain. If a line is imagined on the fluid surface, the fluid on each side of the line try to move far from each other. So, a tension generates on each side of the line. That is surface tension.
So, the cohesive force or the intermolecular attraction creates surface tension in a fluid.
A: This completely depends on the inertia and entropy of the fluid. An air boundary in a barrell of a double overhead ocean wave has a very different surface density compared to say the skin of liquid on a shallow puddle. The closer to chaotic motion should lean towards less dense... ie distance divers will have air jets in pools to break the surface tension so if they land wrong its no issue.. where as a surfer may struggle to jump and kick his way through the skin effect on a huge wave :)
