Learning a Lattice is Easier than Learning an Irregular Graph (Sometimes)

If you made a picture of your social network, what would it look like? Would it look like a regular structure, like a lattice? Or would there be strange detours and crazy long-range connections between your friends’ friends?

Jason's Friendship Network

Jason's Friendship Network

It would probably be something more like the irregular graph than the lattice. People don’t form friendships in a regular, orderly manner conforming to strict rules of structure. Instead, people form local clusters of friends (you can call them cliques) and some people act as bridges between cliques to connect them and form the small-world topography familiar to social networks.

Ring Lattice Network

Ring Lattice Network

This is one of the points Watts and Strogatz illustrated with their social network models. A ring lattice may be a poor analog for a real-life friendship network, but a ring lattice with a few perturbations of the edges does a good job of capturing two characteristics of social graphs: local structure and random edges that allow a small world.

Watts & Strogatz Perturbations of a Ring Lattice

Watts & Strogatz Perturbations of a Ring Lattice

What would happen if we asked people to learn “who is friends with whom” in a ring-lattice social network or a perturbed Watts & Strogatz network? Will the regularity of the lattice structure make it easier to learn, or will it be difficult to learn because it goes against one’s expectations of how friendship clusters work?

The answer depends on the mode of presentation of the network. If the network is presented visually, as a network diagram, subjects learn the perfect Ring Lattice more easily than the perturbed version. However, if the network is presented simply as a list of connected nodes, the two graphs are equally easy (or hard) to acquire.

Accuracy by Training Type and Graph Type

Accuracy by Training Type and Graph Type

Diagram training allows for simple strategies. Names that are close together spatially in a Ring Lattice diagram are necessarily friends. This is true to some degree for the perturbed lattice as well, but it is not as reliable a strategy.

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